Search

The continuous Hopfield network (CHN) is a common recurrent neural network. The CHN tool can be used to solve a number of ranking and optimization problems, where the equilibrium states of the ordinary differential equation (ODE) related to the CHN give the solution to any given problem. Because of the non-local characteristic of the "infinite memory" effect, fractional-order (FO) systems have been proved to describe more accurately the behavior of real dynamical systems, compared to the model's ODE. In this paper, a fractional-order variant of a Hopfield neural network is introduced to solve a Quadratic Knap Sac Problem (QKSP), namely the fractional CHN (FRAC-CHN). Firstly, the system is integrated with the quadratic method for fractional-order equations whose trajectories have shown erratic paths and jumps to other basin attractions. To avoid these drawbacks, a new algorithm for obtaining an equilibrium point for a CHN is introduced in this paper, namely the optimal fractional CHN (OPT-FRAC-CHN). This is a variable time-step method that converges to a good local minima in just a few iterations. Compared with the non-variable time-stepping CHN method, the optimal time-stepping CHN method (OPT-CHN) and the FRAC-CHN method, the OPT-FRAC-CHN method, produce the best local minima for random CHN instances and for the optimal feeding problem. [ABSTRACT FROM AUTHOR]

To construct a nonlinear fractional-order neural network reflecting the complex environment of the real world, this paper considers the common factors such as uncertainties, perturbations, and delays that affect the stability of the network system. In particular, not only does the activation function include multiple time delays, but the memristive connection weights also consider transmission delays. Stemming from the characteristics of neural networks, two different types of discontinuous controllers with state information and sign functions are devised to effectuate network synchronization objectives. Combining the finite-time convergence criterion and the theory of fractional-order calculus, Mittag-Leffler synchronization conditions for fractional-order multi-delayed memristive neural networks (FMMNNs) are derived, and the upper bound of the setting time can be confirmed. Unlike previous jobs, this article focuses on applying different inequality techniques in the synchronous analysis process, rather than comparison principles to manage the multi-delay effects. In addition, this study removes the restrictive requirement that the activation function has a zero value at the switching jumps, and the discontinuous control protocol in this paper makes the networks achieve synchronization over a finite time, with some advantages in terms of the convergence speed. [ABSTRACT FROM AUTHOR]

Radio Frequency IDentification (RFID) Network Planning (RNP) is the problem of placing RFID readers in a working area where a tag is interrogated by at least one reader and at the same time satisfies some constraints such as minimum number of placed readers, minimal interference, and minimal outside coverage. The RNP optimization has been proven NP-hard; thus, natural-inspired approaches are often used to find the optimal solution. The paper proposes an energy-efficient RNP approach in which the positions of placed readers are optimized by a Hopfield network, and the energy efficiency is achieved through a placement area restriction technique. A mechanism of redundant reader elimination is also added to minimize the number of placed readers. Simulation results show that the Hopfield network-based energy-efficient RNP approach achieves the maximum tag coverage and energy efficiency by reducing interference, outside coverage, and the number of placed readers. [ABSTRACT FROM AUTHOR]

The brain, an exceedingly intricate information processing system, poses a constant challenge to memory research, particularly in comprehending how it encodes, stores, and retrieves information. Cognitive psychology studies memory mechanism from behavioral experiment level and fMRI level, and neurobiology studies memory mechanism from anatomy and electrophysiology level. Current research findings are insufficient to provide a comprehensive, detailed explanation of memory processes within the brain. Numerous unknown details must be addressed to establish a complete information processingmechanismconnecting micro molecular cellular levels with macro cognitive behavioral levels. Key issues include characterizing and distributing content within biological neural networks, coexisting information with varying content, and sharing limited resources and storage capacity. Compared with the hard disk of computer mass storage, it is very clear from the polarity of magnetic particles in the bottom layer, the division of tracks and sectors in the middle layer, to the directory tree and file management system in the high layer, but the understanding of memory is not sufficient. Biological neural networks are abstracted as directed graphs, and the encoding, storage, and retrieval of information within directed graphs at the cellular level are explored. A memory computational model based on active directed graphs and node-adaptive learning is proposed. First, based on neuronal local perspectives, autonomous initiative, limited resource competition, and other neurobiological characteristics, a resource-based adaptive learning algorithm for directed graph nodes is designed. To minimize resource consumption of memory content in directed graphs, two resource-occupancy optimization strategies--lateral inhibition and path pruning--are proposed. Second, this paper introduces a novel memory mechanism grounded in graph theory, which considers connected subgraphs as the physical manifestation of memory content in directed graphs. The encoding, storage, consolidation, and retrieval of the brain's memory system correspond to specific operations such as forming subgraphs, accommodating multiple subgraphs, strengthening connections and connectivity of subgraphs, and activating subgraphs. Lastly, a series of experiments were designed to simulate cognitive processes and evaluate the performance of the directed graph model. Experimental results reveal that the proposed adaptive connectivity learning algorithm for directed graphs in this paper possesses the following four features: (1) Demonstrating distributed, self-organizing, and self-adaptive properties, the algorithm achieves global-level functions through local node interactions; (2) Enabling incremental storage and supporting continuous learning capabilities; (3) Displaying stable memory performance, it surpasses the Hopfield network in memory accuracy, capacity, and diversity, as demonstrated in experimental comparisons. Moreover, itmaintains highmemory performance with large-scale datasets; (4) Exhibiting a degree of generalization ability, the algorithm's macroscopic performance remains unaffected by the topological structure of the directed graph. Large-scale, decentralized, and node-autonomous directed graphs are suitable simulation methods. Examining storage problems within directed graphs can reveal the essence of phenomena and uncover fundamental storage rules hidden within complex neuronal mechanisms, such as synaptic plasticity, ion channels, neurotransmitters, and electrochemical activities. [ABSTRACT FROM AUTHOR]

This paper centers on stochastic Hopfield neural networks with variable coefficients and infinite delay. First, we propose an integral inequality that improves and extends some existing works. Second, by employing some inequalities and stochastic analysis techniques, some suffcient conditions for ensuring pth moment generalized exponential stability are established. Our results do not necessitate the construction of a complex Lyapunov function or rely on the assumption of bounded variable coeffscients, and our results expand some existing works. At last, to illustrate the efficacy of our result, we present several simulation examples. [ABSTRACT FROM AUTHOR]

The activation function is crucial in the Hopfield neural network (HNN) to restrict the input–output relation of each neuron. The physical realizability and simplicity of the hardware circuit of activation function are beneficial to promote the practical engineering application of the HNN. However, the HNN commonly used hyperbolic tangent activation function involves a complex hardware circuit implementation. This paper discusses a piecewise-linear activation function (PWL-AF) with simplified circuit implementation and a tri-neuron small-world HNN is built as a paradigm. The hardware implementation circuit of the HNN is greatly simplified, benefited from the PWL-AF with a simple analog circuit. Meanwhile, the dynamics related to the PWL-AF and initial conditions are numerically explored. The numerical results demonstrate that the PWL-AF-based HNN can produce dynamical behaviors like the HNN based on the hyperbolic tangent activation function. Nevertheless, the multistability with up to six kinds of coexisting multiple attractors emerged because of the PWL-AF breakpoint. This can give more flexible and potential aspects in multistability-based engineering applications. Especially, the PWL-AF breakpoint value simultaneously acts as the offset booster and amplitude controller in regulating the offset boosting and amplitude rescaling of neuron states. Afterwards, an analog circuit with three straightforward operational amplifiers (op-amp)-based circuit modules is designed for the PWL-AF, and a PCB-based analog circuit is thereby implemented for the tri-neuron small-world HNN. The hardware experiments agree with the numerical simulations, implying the feasibility of the PWL-AF simplification for the HNN. [ABSTRACT FROM AUTHOR]

In this paper, a dynamic HIV model with cell-to-cell transmission, two immune responses, and induced apoptosis is proposed and studied. First, the non-negativity and boundedness of the solutions of the model are given, and then the exact expression of the basic reproduction number R0 is obtained by using the next generation matrix method. Second, criteria are obtained for the local stability of the disease-free equilibrium, immune response-free equilibrium, and the infected equilibrium with both humoral and cellular immune responses. Furthermore, the threshold conditions are also derived for the global asymptotic stability of the disease-free equilibrium, immune responsefree equilibrium, and the infected equilibrium with both humoral and cellular immune responses by constructing the suitable Lyapunov function. Finally, some numerical simulations are conducted to verify the theoretical results; the numerical simulation results show that the increase of apoptosis rate had a positive role in the control of viral infection. [ABSTRACT FROM AUTHOR]

This paper proposes a new H ∞ static output feedback control method to address the congestion control problem in transmission control protocol networks using active queue management routers. Based on linear matrix inequality optimization, this method determines a static output feedback control law to minimize the H ∞ norm of the transfer function between the controlled queue length of the buffer and the exogenous disturbance affecting the available link bandwidth. A linear matrix inequality formulation is presented as a sufficient condition to guarantee the closed-loop system's asymptotic stability while maintaining disturbance rejection within a specified level, regardless of round-trip time delays. The proposed robust static output feedback control eliminates the need to measure or estimate all system states, thus simplifying practical implementation. The effectiveness of the proposed design method is demonstrated by applying it in a practical process, as illustrated through a numerical example. [ABSTRACT FROM AUTHOR]

Economic growth is resulting in serious environmental problems. Effectively establishing an economic growth model that considers environmental pollution is an important topic. To analyze the interplay between economic growth and environmental pollution, a fractional-order time-delayed economic growth model with environmental purification is proposed in this paper. The established model considers not only the environment and economic production but also the labor force population and total factor productivity. Furthermore, the asymptotic stability conditions and parameter stability interval are provided. Finally, in numerical experiments, the correctness of the theory is verified. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the dynamics of Hopfield neural networks with impulsive effects, focusing on Poisson stable rates, synaptic connections, and unpredictable external inputs. Through the symmetry of impulsive and differential compartments of the model, we follow and extend the principal dynamical ideas of the founder. Specifically, the research delves into the phenomena of unpredictability and Poisson stability, which have been examined in previous studies relating to models of continuous and discontinuous neural networks with constant components. We extend the analysis to discontinuous models characterized by variable impulsive actions and structural ingredients. The method of included intervals based on the B-topology is employed to investigate the networks. It is a novel approach that addresses the unique challenges posed by the sophisticated recurrence. [ABSTRACT FROM AUTHOR]

This paper is devoted to dealing with the issue of the estimation of the domain of attraction (DOA) for highly nonlinear neutral complex networks (HNNCNs) with time delays. Firstly, by the Razumikhin approach, we establish several novel lemmas on the estimation of DOA for highly nonlinear neutral differential systems. The cases of bounded non-differentiable delays and unbounded proportional delays are discussed, respectively. Subsequently, by utilizing the proposed lemmas, combining the Lyapunov stability theory and inequality technique, the estimation of DOA on HNNCNs with bounded delays or proportional delays is derived when the chosen control gain is sufficiently large. If initial values start from DOA, then the states of systems will exponentially or polynomially converge to the equilibrium point, which means that the local exponential or polynomial synchronization of HNNCNs is realized. Additionally, the weighted outer-coupling matrix of complex networks is not required to be symmetric, which means that the derived results can be applied to both the undirected networks and directed networks. Finally, several numerical examples are provided to illustrate the feasibility of theoretical findings. [ABSTRACT FROM AUTHOR]

This paper tries to study the problem of finite-time synchronization for delayed semi-Markov reaction–diffusion systems. Based on the spatial and parametric characteristics of the considered systems, a new asynchronous boundary control scheme is proposed to ensure the finite-time synchronization of the drive and response systems. In the asynchronous boundary control scheme, only an actuator should be placed at the spatial boundary, which is more easier to implement and economical than the other non-boundary control strategies. Besides, the system parameters and controller follow two asynchronous semi-Markov chains for jumping, which is more practical than obeying one semi-Markov chain. Moreover, for the considered systems, we proposes a new lemma of finite-time stability, and by employing the inequality methods and variable substitution, we derive the criterion of finite-time synchronization and a correlative corollary. Finally, a numerical example and an application example on secure communication are carried out to support the developed approach. • Our study enriches the related research of semi-Markov RDSs. The obtained results guarantee the finite-time synchronization of semi-Markov RDSs, which is more effective and practical than asymptotic synchronization. • This paper proposes a novel asynchronous boundary control scheme, for the synchronization of semi-Markov RDSs. Compared with existing ones, our control scheme has obvious advantages in realizability and economy. • Based on the existing papers, in the designed controller, a constant is introduced, such that the intense chatter of controller could be reduced. • For the considered systems and designed controller, a new finite-time stability lemma is proposed, which enables the derivation of a finite-time synchronization criterion and a related corollary of this paper. [ABSTRACT FROM AUTHOR]

An important difference between brains and deep neural networks is the way they learn. Nervous systems learn online where a stream of noisy data points are presented in a non-independent, identically distributed way. Further, synaptic plasticity in the brain depends only on information local to synapses. Deep networks, on the other hand, typically use non-local learning algorithms and are trained in an offline, non-noisy, independent, identically distributed setting. Understanding how neural networks learn under the same constraints as the brain is an open problem for neuroscience and neuromorphic computing. A standard approach to this problem has yet to be established. In this paper, we propose that discrete graphical models that learn via an online maximum a posteriori learning algorithm could provide such an approach. We implement this kind of model in a neural network called the Sparse Quantized Hopfield Network. We show our model outperforms state-of-the-art neural networks on associative memory tasks, outperforms these networks in online, continual settings, learns efficiently with noisy inputs, and is better than baselines on an episodic memory task. Brains and neuromorphic systems learn with local learning rules in online-continual learning scenarios. Designing neural networks that learn effectively under these conditions is challenging. The authors introduce a neural network that implements an effective, principled approach to local, online-continual learning on associative memory tasks. [ABSTRACT FROM AUTHOR]

Linear assignment problems hold a pivotal role in combinatorial optimization, offering a broad spectrum of applications within the field of data sciences. They consist of assigning "agents" to "tasks" in a way that leads to a minimum total cost associated with the assignment. The assignment is balanced when the number of agents equals the number of tasks, with a one-to-one correspondence between agents and tasks, and it is and unbalanced otherwise. Additional options and constraints may be imposed, such as allowing agents to perform multiple tasks or allowing tasks to be performed by multiple agents. In this paper, we propose a novel framework that can solve all these assignment problems employing methodologies derived from the field of statistical physics. We describe this formalism in detail and validate all its assertions. A major part of this framework is the definition of a concave effective free energy function that encapsulates the constraints of the assignment problem within a finite temperature context. We demonstrate that this free energy monotonically decreases as a function of a parameter β representing the inverse of temperature. As β increases, the free energy converges to the optimal assignment cost. Furthermore, we demonstrate that when β values are sufficiently large, the exact solution to the assignment problem can be derived by rounding off the elements of the computed assignment matrix to the nearest integer. We describe a computer implementation of our framework and illustrate its application to multi-task assignment problems for which the Hungarian algorithm is not applicable. [ABSTRACT FROM AUTHOR]

This study investigates the asymptotic synchronization in fractional memristive neural networks of the Riemann–Liouville type, considering mixed time delays and jump mismatches. Addressing the challenges associated with discrepancies in the circuit switching speed and the accuracy of the memristor, this paper introduces an enhanced model that effectively navigates these complexities. We propose two novel event-based hybrid impulsive controllers, each characterized by unique triggering conditions. Utilizing advanced techniques in inequality and hybrid impulsive control, we establish the conditions necessary for achieving synchronization through innovative Lyapunov functions. Importantly, the developed controllers are theoretically optimized to minimize control costs, an essential consideration for their practical deployment. Finally, the effectiveness of our proposed approach is demonstrated through two illustrative simulation examples. [ABSTRACT FROM AUTHOR]

The electro-hydraulic servo system has advantages such as high pressure, large flow, and high power, etc., which can also realize stepless regulation, so it is widely used in many engineering machineries. A linear model is sometimes only a simple approximation of an idealized model, but in an actual system, there may be nonlinear and transient variation characteristics in the systems. Coupling is reflected in the fact that the components or functional structures implemented by each system used for the design of hydraulic systems are not completely or independently related to each other, but affect each other. The nonlinear clearance between the actuator and the load reduces the control accuracy of the system and increases the impact, thus losing stable working conditions. In the paper, based on the nonlinear clearance problem of the electro-hydraulic servo system, a mathematical transfer model with clearance is established, and on this basis, a clearance compensation method based on the Hopfield neural network is proposed. In this way, clearance compensation can be realized by adjusting the parameters of neural network nodes, through simple and convenient operation. Finally, by setting different clearance values, the results of the step response and sine response curve before and after clearance compensation of the hydraulic system are compared, and the effectiveness of Hopfield neural network compensation clearance control is verified based on the comparison simulation results. [ABSTRACT FROM AUTHOR]

Memristor is a kind of nonlinear resistance with memory function, which is a typical nonlinear circuit component. In this paper, the problem of a simple chaotic circuit based on the memristor was studied. We constructed a new simple circuit of multiple memorizing components, summarized the mathematical model and found seven types of chaotic attractors without reference to classical circuits that substituted memristors for elements in the original circuit. Traditional methods of dynamic analysis are used to analyze the equilibrium point and stability of the system. Furthermore, we analyzed the dynamical behavior with the varying coefficient of the system specifically. In order to reduce the deviation from the actual physical circuit system as much as possible so as to facilitate the follow-up research of scholars, we solved the problem of Hopf bifurcation in this system under the condition of time delay through the use of the canonical form and Hopf bifurcation theory. Theoretical analysis and simulation results show that there existed the state transition in seven chaotic attractors of system and the bifurcation was stable when we changed the parameter τ slightly. As a small unit circuit, this paper lays a foundation for the research and control of large-scale system with memorizing components. [ABSTRACT FROM AUTHOR]

For this paper, we consider the almost sure exponential stability of uncertain stochastic Hopfield neural networks based on subadditive measures. Firstly, we deduce two corollaries, using the Itô–Liu formula. Then, we introduce the concept of almost sure exponential stability for uncertain stochastic Hopfield neural networks. Next, we investigate the almost sure exponential stability of uncertain stochastic Hopfield neural networks, using the Lyapunov method, Liu inequality, the Liu lemma, and exponential martingale inequality. In addition, we prove two sufficient conditions for almost sure exponential stability. Furthermore, we consider stabilization with linear uncertain stochastic perturbation and present some exceptional examples. Finally, our paper provides our conclusion. [ABSTRACT FROM AUTHOR]

In this paper, the problem on finite-/fixed-time synchronization (FFTS) is investigated for a class of diffusive Hopfield neural networks with leakage and discrete delays. Some new and useful criteria independent on time delays but dependent on the diffusion coefficients are established to guarantee the FFTS for the addressed network model under a unified framework. In sharp contrast to the existed results which can only finite-timely or fixed-timely synchronize the systems with both diffusion effects and leakage delays, the theoretical results of this paper are more general and practical. Finally, a numerical example is presented to show the effectiveness of the proposed control methods. [ABSTRACT FROM AUTHOR]

With the rapid development of the Internet era and the high popularity of computers, China's economy, politics, and culture have made rapid progress in recent years. In order to adapt to this era of rapid change, China's higher education has also undergone great changes and carried out reform and innovation. As the top priority in the Internet era, computers should be reformed first. The traditional education model is mainly teacher-centered and classroom-centered. The disadvantages of this teaching mode are that students' subjective initiative cannot be fully developed and brought into play. Traditional teaching pays attention to knowledge teaching and ignores ability training. It emphasizes speaking and neglects practice. Therefore, in order to meet the development needs of the new era and cultivate modern talents, colleges and universities began to explore the innovation and entrepreneurship education mode. There is an application of TRIZ theory to the cultivation of innovation and entrepreneurship education, and TRIZ theory is a theory for solving invention problems. Its main content is to find its own laws in the process of technological evolution and analyze the laws to get a general solution, but there are many obstacles in exploring the mode of innovation and entrepreneurship education; for example, many governments do not support this education reform and do not broadcast relevant education and teaching funds for schools, resulting in uneven configuration of software and hardware in schools. According to the survey, the proportion of innovation and entrepreneurship education in the eastern coastal areas is as high as 70%, while the proportion of innovation and entrepreneurship education in the central and western regions is only 10%. This set of data shows that regional differences are the main reason for the differences in education development. In terms of the proportion of education funds, although the annual education funds will gradually increase in recent years, the proportion is still a drop in the bucket in front of huge fiscal revenue, with the highest being only 0.1%. Therefore, in order to improve the current situation of innovation and entrepreneurship education mode in colleges and universities, according to their own characteristics, the reform is carried out from the aspects of practical ability, competition participation, and training plan, and the BP neural network model is introduced to predict and analyze the effect of teaching methods. The results of this paper are investigated and analyzed. Finally, the investigation on the development of KAB course and SYB course and the analysis on the stability and error of BP neural network are within the allowable range, this shows that the model established in this paper is more favored by students than the traditional teaching methods, more in line with the social reality, the effect is more ideal, and the result is more stable. [ABSTRACT FROM AUTHOR]

To reduce the communication and computation overhead of neural networks, a novel pinning event-triggered scheme (PETS) is developed in this paper, which enables pinning synchronization of uncertain coupled memristive neural networks (CMNNs) under limited resources. Time-varying delays, uncertainties, and mismatched parameters are all considered, which makes the system more interpretable. In addition, from the low energy cost point of view, an algorithm for pinned node selection is designed to further investigate the newly event-triggered function under limited communication resources. Meanwhile, based on the PETS and following the Lyapunov functional method, sufficient conditions for the pinning exponential stability of the proposed coupled error system are formulated, and the analysis of the self-triggered method shows that our method can efficiently avoid Zeno behavior under the newly determined triggered conditions, which contribute to better PETS performance. Extensive experiments demonstrate that the PETS significantly outperforms the existing schemes in terms of solution quality. [ABSTRACT FROM AUTHOR]

Combinatorial optimization problems are ubiquitous and computationally hard to solve in general. Quantum approximate optimization algorithm (QAOA), one of the most representative quantum-classical hybrid algorithms, is designed to solve combinatorial optimization problems by transforming the discrete optimization problem into a classical optimization problem over continuous circuit parameters. QAOA objective landscape is notorious for pervasive local minima, and its viability significantly relies on the efficacy of the classical optimizer. In this work, we design double adaptive-region Bayesian optimization (DARBO) for QAOA. Our numerical results demonstrate that the algorithm greatly outperforms conventional optimizers in terms of speed, accuracy, and stability. We also address the issues of measurement efficiency and the suppression of quantum noise by conducting the full optimization loop on a superconducting quantum processor as a proof of concept. This work helps to unlock the full power of QAOA and paves the way toward achieving quantum advantage in practical classical tasks. There is no universal way of optimizing the variation quantum circuits used in Noisy Intermediate-Scale Quantum (NISQ) applications. In this paper the authors introduce a new classical Bayesian optimizer, which converges much more quickly than conventional approaches, and test it for solving the Quantum Approximate Optimization Algorithm (QAOA) problem. [ABSTRACT FROM AUTHOR]

This paper studies the stability criterion and controller design for time-delay switched systems with input saturation. The main contributions of this paper are as follows: (1) Based on constructing the Lyapunov–Krasovskii functional (LKF) with the triple integral term and making full use of the delay lower bound information, the sufficient conditions for the exponential stability of the system are given. (2) A state feedback controller is designed for the input-saturated system. (3) The symmetric delay rate problem is considered to accurately define the derivative of LKF, which reduces the conservatism of the system. By reducing conservatism, that is, the time-delay upper bound is raised, allowing for a wider range of time-delay signals. Finally, the effectiveness of the proposed method is verified by the numerical examples. [ABSTRACT FROM AUTHOR]

Efficient integration of wind energy requires accurate wind power forecasting. This prediction is critical in optimising grid operation, energy trading, and effectively harnessing renewable resources. However, the wind's complex and variable nature poses considerable challenges to achieving accurate forecasts. In this context, the accuracy of wind parameter forecasts, including wind speed and direction, is essential to enhancing the precision of wind power predictions. The presence of missing data in these parameters further complicates the forecasting process. These missing values could result from sensor malfunctions, communication issues, or other technical constraints. Addressing this issue is essential to ensuring the reliability of wind power predictions and the stability of the power grid. This paper proposes a long short-term memory (LSTM) model to forecast missing wind speed and direction data to tackle these issues. A fractional-order neural network (FONN) with a fractional arctan activation function is also developed to enhance generated wind power prediction. The predictive efficacy of the FONN model is demonstrated through two comprehensive case studies. In the first case, wind direction and forecast wind speed data are used, while in the second case, wind speed and forecast wind direction data are used for predicting power. The proposed hybrid neural network model improves wind power forecasting accuracy and addresses data gaps. The model's performance is measured using mean errors and R2 values. [ABSTRACT FROM AUTHOR]

The current development of logic satisfiability in discrete Hopfield neural networks (DHNN)has been segregated into systematic logic and non-systematic logic. Most of the research tends to improve non-systematic logical rules to various extents, such as introducing the ratio of a negative literal and a flexible hybrid logical structure that combines systematic and non-systematic structures. However, the existing non-systematic logical rule exhibited a drawback concerning the impact of negative literal within the logical structure. Therefore, this paper presented a novel class of non-systematic logic called conditional random k satisfiability for k=1,2 while intentionally disregarding both positive literals in second-order clauses. The proposed logic was embedded into the discrete Hopfield neural network with the ultimate goal of minimizing the cost function. Moreover, a novel non-monotonic Smish activation function has been introduced with the aim of enhancing the quality of the final neuronal state. The performance of the proposed logic with new activation function was compared with other state of the art logical rules in conjunction with five different types of activation functions. Based on the findings, the proposed logic has obtained a lower learning error, with the highest total neuron variation TV=857 and lowest average of Jaccard index, JSI=0.5802. On top of that, the Smish activation function highlights its capability in the DHNN based on the result ratio of improvement Zm and TV. The ratio of improvement for Smish is consistently the highest throughout all the types of activation function, showing that Smish outperforms other types of activation functions in terms of Zm and TV. This new development of logical rule with the non-monotonic Smish activation function presents an alternative strategy to the logic mining technique. This finding will be of particular interest especially to the research areas of artificial neural network, logic satisfiability in DHNN and activation function. [ABSTRACT FROM AUTHOR]

In this paper, a new-type time-varying asymmetric integral barrier function is designed to handle the state constraint of nonlinear systems. The barrier Lyapunov function is developed by building an integral upper limit function with respect to transformation errors over an open set to cope with the position constraint of the robotic system. We know that the symmetric time-invariant constraint is only a particular situation of the asymmetric time-variant constraint, and thus compared to existing methods, it is capable of handling more general and broad practical engineering issues. We show that under the integral barrier Lyapunov function combining a disturbance observer-based tracking controller, the position vector tracks a desired trajectory successfully, while the constraint boundary is never violated. It can certify the exponential asymptotic stability of the robotic tracking system by using the given inequality relationship on barrier function and Lyapunov analysis. Finally, the feasibility of the presented algorithm is indicated by completing the simulations. [ABSTRACT FROM AUTHOR]

This paper is concerned with the global asymptotic stability (GAS) problem of fixed-point Lipschitz nonlinear digital filters employing 2's complement overflow arithmetic. Nonlinear digital filtering finds immense applications in various fields such as adaptive systems and controllers, digital controllers and observers for nonlinear systems, realization of neural networks using digital hardware, controllers for feedback linearization, etc. Lipschitz nonlinear digital filter is considered in this paper as it is frequently employed in nonlinear digital filtering, state filtering, neural networks, feedback control, digital controllers, decision-taking systems and so on. Based on Lyapunov theory, the property of 2's complement overflow arithmetic and Lipschitz condition associated with system nonlinearities, a new criterion for the suppression of overflow oscillations in 2's complement state variable realizations of digital filters is established. Several examples along with simulation results are provided to highlight the utility of the criterion. [ABSTRACT FROM AUTHOR]

This paper is concerned with the observer-based H ∞ proportional-integral-derivative (PID) control issue for discrete-time systems using event-triggered mechanism subject to periodic random denial of service (DoS) jamming attacks and infinitely distributed delays. In order to characterize the occurrence of periodic random DoS jamming attacks in the network channel between controller and actuator, the Kronecker delta function is used to represent the periodic switching between the sleeping period and attack period, and a Bernoulli-distributed random variable is utilized to reflect the probabilistic occurrence of DoS attacks. Infinitely distributed delay is involved to reflect actual state lag. The relative event-triggering mechanism is employed to reduce unnecessary information transmission and save communication energy in the network channel between sensor and observer. An observer-based PID controller is constructed for the regulation of the system to achieve an appropriate working effect. The aim of this paper is to design a security-guaranteed PID controller for delayed systems such that both the exponential mean-square stability and the H ∞ performance are satisfied. Using the Lyapunov stability theory, stochastic analysis method and matrix inequality technique, a sufficient condition is put forward that ensures the existence of the required observer and PID controller. Gain parameters of the observer and the PID controller are computed by solving a certain matrix inequality. A simulation is carried out to verify the effectiveness of the developed observer-based H ∞ PID control method. The obtained H ∞ noise rejection level is below 0.85 , the average event-based release interval is 13, the absolute values of the maximum estimation error of two elements in the system state are 1.434 and 0.371 using the observer, and two elements of the system state converge to 0.238 and − 0.054 at the 41th time step with two elements of the control output being 0.031 and 0.087 . [ABSTRACT FROM AUTHOR]

In this paper, we establish a random epidemic model with double vaccination and spontaneous variation of the virus. Firstly, we prove the global existence and uniqueness of positive solutions for a stochastic epidemic model. Secondly, we prove the threshold R 0 * can be used to control the stochastic dynamics of the model. If R 0 * < 0 , the disease will be extinct with probability 1; whereas if R 0 * > 0 , the disease can almost certainly continue to exist, and there is a unique stable distribution. Finally, we give some numerical examples to verify our theoretical results. Most of the existing studies prove the stochastic dynamics of the model by constructing Lyapunov functions. However, the construction of a Lyapunov function of higher-order models is extremely complex, so this method is not applicable to all models. In this paper, we use the definition method suitable for more models to prove the stationary distribution. Most of the stochastic infectious disease models studied now are second-order or third-order, and cannot accurately describe infectious diseases. In order to solve this kind of problem, this paper adopts a higher price five-order model. [ABSTRACT FROM AUTHOR]

In recent years, cellular neural networks (CNNs) have become a popular apparatus for simulations in neuroscience, biology, medicine, computer sciences and engineering. In order to create more adequate models, researchers have considered memory effects, reaction–diffusion structures, impulsive perturbations, uncertain terms and fractional-order dynamics. The design, cellular aspects, functioning and behavioral aspects of such CNN models depend on efficient stability and control strategies. In many practical cases, the classical stability approaches are useless. Recently, in a series of papers, we have proposed several extended stability and control concepts that are more appropriate from the applied point of view. This paper is an overview of our main results and focuses on extended stability and control notions including practical stability, stability with respect to sets and manifolds and Lipschitz stability. We outline the recent progress in the stability and control methods and provide diverse mechanisms that can be used by the researchers in the field. The proposed stability techniques are presented through several types of impulsive and fractional-order CNN models. Examples are elaborated to demonstrate the feasibility of different technologies. [ABSTRACT FROM AUTHOR]

In this paper, by using Lyapunov-Krasovskii stability theory and linear matrix inequality approach, the control problem for fractional-order systems under seismic waveswith time-varying delays is studied. A novel switching surface is proposed. Based on the linear quadratic regulator and sliding mode control, some sufficient conditions are derived to ensure the fractional system under control. Mittag-Leffler stability theorem is adopted to prove that the switching surface could converge to zero. Finally, a numerical simulation example is provided to validate the advantages and effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

This paper extends the method originally proposed in [1] to systems with an arbitrary number of inputs and outputs. The method ensures that these signals will be in given domains. Two sequential changes of coordinates are introduced to solve the problem. The first change reduces the plant's output to a new variable of a dimension not exceeding that of the control vector (input). The second change allows passing from the control problem with constraints to the one without them. The effectiveness of this method is illustrated for two problems. The first problem is designing a state-feedback controller for linear systems with constraints imposed on the input and state variables. The second problem is designing an output-feedback controller for linear systems with constraints imposed on the output and input. In both problems, the stability of the closed loop system is verified in terms of linear matrix inequalities. The results are accompanied by simulation examples to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, the robust stabilization for the networked microgrid system is presented. A microgrid implements master-slave control architecture where the communication channel is utilized to exchange the reference current signals. With this structure, a time delay exists in the reference control signal which may lead to instability. The analysis of the control strategy is carried out in dq reference frame. The microgrid is constituted by PV and wind energy sources supplying a load through voltage source inverters. The stochastic nature of renewable energy sources introduces uncertainties which can be represented as fluctuations in the voltage and the current. The main contribution of the paper is formulating the controller design of the microgrid with communication delay and uncertainties in the model as H∞ control problem and Lyapunov–Krasovskii functional is utilized to develop stability criterion in bilinear matrix inequality form. Grey wolf optimizer is used to minimize the performance index and derive the stabilizing controller. The microgrid performance is tested through simulation using the time-varying nonlinear model of the microgrid. The results prove that satisfactory current and power-sharing are attained even with the existence of time delays and uncertainties. [ABSTRACT FROM AUTHOR]

In this paper, we are interested in the finite-time synchronization of complex-valued BAM neural networks with time delays. Without applying Lyapunov–Krasovskii functional theory, finite-time convergence theorem, graph-theoretic method, the theory of complex functions or the integral inequality method, by using the quadratic analysis approach, inequality techniques and designing two classes of novel controllers, two novel sufficient conditions are achieved to guarantee finite-time synchronization between the master system and the slave system. The quadratic analysis method used in our paper is a different study approach of finite-time synchronization from those in existing papers. Therefore the controllers designed in our paper are fully novel. [ABSTRACT FROM AUTHOR]

This paper analyzes the fingerprint characteristics of a memristor model and proves that this memristor model conforms to the definition of generalized memristor. Using this memristor model, a new class of memristive circuit is built. A new memristive system is obtained through the mathematical modeling of the memristive circuit. The equilibrium points and stability of the new memristive system are analyzed by mathematical theory, and the complex dynamic behavior of the system under different parameters is analyzed by using simulation tools such as phase diagram, bifurcation diagram, Lyapunov exponent spectrum and time-domain waveform. Through simulation, it is found that this system can have quasi-periodic, periodic, chaotic and hyperchaotic attractors and wing-variable phenomenon under the change of parameters. The sensitivity of hyperchaos and chaos to the change of initial value is studied, and the phenomena of chaotic bursting and periodic bursting are observed. For physical verification, the hardware implementation of digital circuit based on FPGA is given. The experimental results are consistent with the numerical simulation ones, which prove its physical realizability. [ABSTRACT FROM AUTHOR]

The fingerprint indoor localization method based on channel state information (CSI) has gained widespread attention. However, this method fails to provide a better localization effect and higher localization accuracy due to poor fingerprint accuracy, unsatisfactory classification and matching effect, and vulnerability to environmental impacts. In order to solve the problem, this paper proposes a CSI fingerprint indoor localization method based on the Discrete Hopfield Neural Network (DHNN). The method mainly consists of off-line and on-line phases. At the off-line phase, a low-pass filter is applied to conduct a preliminary processing on the fingerprint information of each reference point, and then, phase difference is adopted to correct the fingerprint data of all reference points. In this way, the quality of fingerprint data is improved, hence avoiding problems such as indoor environmental changes and multipath effect of signals, etc. in which impact the fingerprint data. Finally, the characteristic fingerprint database is established after acquiring relatively accurate fingerprint data. At the on-line phase, to maintain the consistency of data, the data of each reference point in the fingerprint database is set as an attractor. Meanwhile, the localization information of the test point is processed to make convergence judgment through DHNN. Eventually, the localization result is obtained. The experimental results show that the localization accuracy with a median error of 1.6 m can be achieved through the proposed method in the experimental environment. Compared with similar methods, it has a higher stability which can significantly reduce the cost of manpower and time. [ABSTRACT FROM AUTHOR]

Alternative paradigms to the von Neumann computing scheme are currently arousing huge interest. Oscillatory neural networks (ONNs) using emerging phase-change materials like VO2 constitute an energy-efficient, massively parallel, brain-inspired, in-memory computing approach. The encoding of information in the phase pattern of frequency-locked, weakly coupled oscillators makes it possible to exploit their rich non-linear dynamics and their synchronization phenomena for computing. A single fully connected ONN layer can implement an auto-associative memory comparable to that of a Hopfield network, hence Hebbian learning rule is the most widely adopted method for configuring ONNs for such applications, despite its well-known limitations. An extensive amount of literature is available about learning in Hopfield networks, with information regarding many different learning algorithms that perform better than the Hebbian rule. However, not all of these algorithms are useful for ONN training due to the constraints imposed by their physical implementation. This paper evaluates different learning methods with respect to their suitability for ONNs. It proposes a new approach, which is compared against previous works. The proposed method has been shown to produce competitive results in terms of pattern recognition accuracy with reduced precision in synaptic weights, and to be suitable for online learning. [ABSTRACT FROM AUTHOR]

In this paper, we proposed and studied a simple five-dimensional mathematical model that describes the second and third stages of the anaerobic degradation process under the influence of leachate recirculation. The state variables are the concentration of insoluble substrate, soluble substrate, produced hydrogen, acetogenic bacteria and hydrogenotrophic-methanogenic bacteria. The growth rates of used bacteria will be of general nonlinear form. The stability of the steady states will be studied by reducing the model to a 3D system. According to the operating parameters of the bioreactor described by the added insoluble substrate, soluble substrate and hydrogen input concentrations and the dilution rate, we proved that the model can admit multiple equilibrium points and we gave the necessary and sufficient assumptions for their existence, their uniqueness and their stability. In particular, the uniform persistence of the system was satisfied under some natural assumptions on the growth rates. Then, a question was answered related to the management of renewable resources where the goal of was to propose an optimal strategy of leachate recirculation to reduce the organic matter (either soluble or insoluble) and keep a limitation of the costs of the recirculation operation during the process. The findings of this work were validated by an intensive numerical investigation. [ABSTRACT FROM AUTHOR]

Fractional calculus research indicates that, within the field of neural networks, fractional-order systems more accurately simulate the temporal memory effects present in the human brain. Therefore, it is worthwhile to conduct an in-depth investigation into the complex dynamics of fractional-order neural networks compared to integer-order models. In this paper, we propose a magnetically controlled, memristor-based, fractional-order chaotic system under electromagnetic radiation, utilizing the Hopfield neural network (HNN) model with four neurons as the foundation. The proposed system is solved by using the Adomain decomposition method (ADM). Then, through dynamic simulations of the internal parameters of the system, rich dynamic behaviors are found, such as chaos, quasiperiodicity, direction-controllable multi-scroll, and the emergence of analogous symmetric dynamic behaviors in the system as the radiation parameters are altered, with the order remaining constant. Finally, we implement the proposed new fractional-order HNN system on a field-programmable gate array (FPGA). The experimental results show the feasibility of the theoretical analysis. [ABSTRACT FROM AUTHOR]

The direct current (DC) microgrid is one of the key research areas for our advancement toward carbon-free energy production. In this paper, a two-step controller is designed for the DC microgrid using a combination of the deep neural network (DNN) and exponential reaching law-based global terminal sliding mode control (ERL-GTSMC). The DC microgrid under consideration involves multiple renewable sources (wind, PV) and an energy storage unit (ESU) connected to a 700 V DC bus and a 4–12 kW residential load. The proposed control method eliminates the chattering phenomenon and offers quick reaching time by utilizing the exponential reaching law (ERL). In the two-step control configuration, first, DNNs are used to find maximum power point tracking (MPPT) reference values, and then ERL-based GTSMC is utilized to track the reference values. The real dynamics of energy sources and the DC bus are mathematically modeled, which increases the system's complexity. Through the use of Lyapunov stability criteria, the stability of the control system is examined. The effectiveness of the suggested hybrid control algorithm has been examined using MATLAB simulations. The proposed framework has been compared to traditional sliding mode control and terminal sliding mode control to showcase its superiority and robustness. Experimental tests based on the hardware-in-the-loop (HIL) setup are then conducted using 32-bit TMS320F28379D microcontrollers. Both MATLAB and HIL results show strong performance under a range of environmental circumstances and system uncertainties. [ABSTRACT FROM AUTHOR]

This paper studies the asymptotic stability of fractional-order neural networks (FONNs) with time delay utilizing a sampled-data controller. Firstly, a novel class of Lyapunov–Krasovskii functions (LKFs) is established, in which time delay and fractional-order information are fully taken into account. Secondly, by combining with the fractional-order Leibniz–Newton formula, LKFs, and other analysis techniques, some less conservative stability criteria that depend on time delay and fractional-order information are given in terms of linear matrix inequalities (LMIs). In the meantime, the sampled-data controller gain is developed under a larger sampling interval. Last, the proposed criteria are shown to be valid and less conservative than the existing ones using three numerical examples. [ABSTRACT FROM AUTHOR]

This paper studies gene regulatory networks (GRNs) with distributed delays. The essential concept of practical stability of the genes is introduced. We investigate the problems of practical stability and global practical exponential stability of the GRN model under an impulsive control. New practical stability criteria are proposed by designing appropriate impulsive controllers via the Lyapunov functions approach. In the design of the impulsive controller, we consider the effect of impulsive perturbations at fixed times and distributed delays on the stability of the considered GRNs. Several numerical examples are also presented to justify the proposed criteria. [ABSTRACT FROM AUTHOR]

The attention mechanism empowers deep learning to a broader range of applications, but the contribution of the attention module is highly controversial. Research on modern Hopfield networks indicates that the attention mechanism can also be used in shallow networks. Its automatic sample filtering facilitates instance extraction in Multiple Instances Learning tasks. Since the attention mechanism has a clear contribution and intuitive performance in shallow networks, this paper further investigates its optimization method based on the recurrent neural network. Through comprehensive comparison, we find that the Synergetic Neural Network has the advantage of more accurate and controllable convergences and revertible converging steps. Therefore, we design the Syn layer based on the Synergetic Neural Network and propose the novel invertible activation function as the forward and backward update formula for attention weights concentration or distraction. Experimental results show that our method outperforms other methods in all Multiple Instances Learning benchmark datasets. Concentration improves the robustness of the results, while distraction expands the instance observing space and yields better results. Codes available at https://github.com/wzh134/Syn. [ABSTRACT FROM AUTHOR]

Nowadays, multi-access edge computing (MEC) has been widely recognized as a promising technology that can support a wide range of new applications for the Internet of Things (IoT). In dynamic MEC networks, the heterogeneous computation capacities of the edge servers and the diversified requirements of the IoT applications are both asymmetric, where and when to offload and schedule the time-dependent tasks of IoT applications remains a challenge. In this paper, we propose a flexible offloading and task scheduling scheme (FLOATS) to adaptively optimize the computation of offloading decisions and scheduling priority sequences for time-dependent tasks in dynamic networks. We model the dynamic optimization problem as a multi-objective combinatorial optimization problem in an infinite time horizon, which is intractable to solve. To address this, a rolling-horizon-based optimization mechanism is designed to decompose the dynamic optimization problem into a series of static sub-problems. A genetic algorithm (GA)-based computation offloading and task scheduling algorithm is proposed for each static sub-problem. This algorithm encodes feasible solutions into two-layer chromosomes, and the optimal solution can be obtained through chromosome selection, crossover and mutation operations. The simulation results demonstrate that the proposed scheme can effectively reduce network costs in comparison to other reference schemes. [ABSTRACT FROM AUTHOR]

Exponential stability criteria for neutral second-order stochastic systems involving impulses and state-dependent delay have been addressed in this paper based on stability theory, stochastic analysis, and the inequality technique. Some sufficient conditions are given to establish the exponential stability of such systems, which is well-established in the deterministic case, but less known for the stochastic case. In our model, the noise effect can be described as a symmetric Wiener process. By formulating the impulsive integral technique, exponential stability analysis of the pth moment of the second-order system involving stochastic perturbation is established. As an application that illustrates the theoretical formulation, an example is presented. [ABSTRACT FROM AUTHOR]

This paper investigates the stabilization problem of switched systems with mismatched modes by an event-triggered control approach. A hybrid event-triggered scheme (HETS) with a dynamically adjustable threshold is newly proposed, which combines periodic sampling, continuous event-trigger and slow switching. It is assumed that the modes and states of the controller are updated only at each triggering instant, so the situation of asynchronous switching could arise. Compared with the control strategy under static HETS, the proposed hybrid event-triggered control strategy has the advantage of potentially speeding up the stabilization while reducing the communication burden. To ease the analysis, the closed-loop system is accordingly represented as a combination of the switched system with a periodically sampled control input and the one with a continuously event-triggered control input. By considering input delay information in the construction of multiple Lyapunov–Krasovskii functional (LKF), a discontinuous and non-positive definite LKF is developed to establish sufficient conditions on the exponential stability for the closed-loop switched system. The design method of the desired controller and HETS is then provided. Finally, the result obtained in this paper is applied to a networked continuous stirred tank reactors system. • A hybrid event-triggered control scheme is newly proposed for the switched systems. • Based on the scheme, a special closed-loop system is presented to ease the analysis. • Multiple Lyapunov–Krasovskii functional with less constraint is developed. • The result is finally applied to a networked continuous stirred tank reactors system. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the multiplicity of positive periodic solutions of a discrete blood cell production model with impulse effects. This model is described by periodic coefficients and time delays, as well as nonlinear feedback with exponential terms. By employing the Krasnosel'skii fixed point theorem, we establish a sufficient condition for the existence of at least two positive periodic solutions. To this end, we construct solution transformation between an impulsive delay difference equation and the corresponding nonimpulsive delay difference equation. Aditionally, a solution representation of the positive periodic solution of the blood cell production model is presented. Moreover, a numerical example and its simulations are given to illustrate the main result. [ABSTRACT FROM AUTHOR]

This paper presents a study on a memristive two-neuron-based Hopfield neural network with fractional-order derivatives. The equilibrium points of the system are identified, and their stability is analyzed. Bifurcation diagrams are obtained by varying the magnetic induction strength and the fractional-order derivative, revealing significant changes in the system dynamics. It is observed that lower fractional orders result in an extended bistability region. Also, chaos is only observed for larger magnetic strengths and fractional orders. Additionally, the application of the fractional-order model for image encryption is explored. The results demonstrate that the encryption based on the fractional model is efficient with high key sensitivity. It leads to an encrypted image with high entropy, neglectable correlation coefficient, and uniform distribution. Furthermore, the encryption system shows resistance to differential attacks, cropping attacks, and noise pollution. The Peak Signal-to-Noise Ratio (PSNR) calculations indicate that using a fractional derivative yields a higher PSNR compared to an integer derivative. [ABSTRACT FROM AUTHOR]

In this paper, we study a model that enhances our understanding of cytokine-influenced HIV-1 infection. The impact of adaptive immune response (cytotoxic T lymphocytes (CTLs) and antibodies) and time delay on HIV-1 infection is included. The model takes into account two types of distributional delays, (i) the delay in the HIV-1 infection of CD4+T cells and (ii) the maturation delay of new virions. We first investigated the fundamental characteristics of the system, then found the system's equilibria. We derived five threshold parameters, ℜ i , i = 0, 1,..., 4, which completely determine the existence and stability of the equilibria. The Lyapunov method was used to prove the global asymptotic stability for all equilibria. We illustrate the theoretical results by performing numerical simulations. We also performed a sensitivity analysis on the basic reproduction number ℜ 0 and identified the most-sensitive parameters. We found that pyroptosis contributes to the number ℜ 0 , and then, neglecting it will make ℜ 0 underevaluated. Necrosulfonamide and highly active antiretroviral drug therapy (HAART) can be effective in preventing pyroptosis and at reducing viral replication. Further, it was also found that increasing time delays can effectively decrease ℜ 0 and, then, inhibit HIV-1 replication. Furthermore, it is shown that both CTLs and antibody immune responses have no effect on ℜ 0 , while this can result in less HIV-1 infection. [ABSTRACT FROM AUTHOR]

This paper formulates and analyzes two mathematical models that describe the within-host dynamics of human immunodeficiency virus type 1 (HIV-1) with impairment of both cytotoxic T lymphocytes (CTLs) and B cells. Both viral transmission (VT) and cellular infection (CT) mechanisms are considered. The second model is a generalization of the first model that includes distributed time delays. For the two models, we establish the non-negativity and boundedness of the solutions, find the basic reproductive numbers, determine all possible steady states and establish the global asymptotic stability properties of all steady states by means of the Lyapunov method. We confirm the theoretical results by conducting numerical simulations. We conduct a sensitivity analysis to show the effect of the values of the parameters on the basic reproductive number. We discuss the results, showing that impaired B cells and CTLs, time delay and latent CT have significant effects on the HIV-1 dynamics. [ABSTRACT FROM AUTHOR]