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In this paper, we present a novel approach for discretizing the derivative Nonlinear Schrödinger (DNLS) equation in an integrable manner. Our proposed method involves discretizing the time variable, resulting in a discrete system that converges to the DNLS equation in a natural limit. Furthermore, the discrete system retains the same set of infinitely conserved quantities as the original DNLS equation. To demonstrate the effectiveness of our proposed method, we designed a numerical simulation scheme using the Fourier Pseudo-spectral Method to discretize the spatial variable. The numerical results confirm that our new discrete integrable scheme can accurately preserve the conserved quantities of the DNLS equation. [ABSTRACT FROM AUTHOR]

In this paper, considering the spatial propagation behavior of Internet rumor, we propose a new reaction–diffusion rumor propagation model with time delay in social networks. Based on this, we discuss the stability conditions at the equilibrium point and analyze the Turing instability for the approximation propagation system. Simultaneously, the amplitude equations for the approximation system are derived by multiscale analysis. We use numerical simulation to compare the effect of parameter size, period, and time delay on the patterns. Moreover, we compare the different reactivity of the system in the W S networks and the B A networks. Finally, we plot the corresponding amplitude equations patterns by controlling the parameters and verify the correctness of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the dynamic feedback design for linear systems with input disturbance. We propose a new approach to design dynamic feedback such that the disturbance in the control channel can be compensated effectively. An interesting characteristic about the disturbance robustness of dynamic feedback is found. Thanks to this interesting characteristic, we just need to consider the disturbance-free system to make the dynamic feedback design. This fact is well validated by several dynamic feedback laws proposed in this paper. Our results are available for the regular linear system with harmonic disturbance. Moreover, the stabilization of an unstable heat equation with general periodic disturbance is also investigated. In order to validate the theoretical results visually, some numerical simulations are given to show the effectiveness of the proposed dynamic feedback. [ABSTRACT FROM AUTHOR]

In this paper, we construct an improved Implicit–Explicit (IMEX) numerical scheme based on the conservation form of the advection–diffusion equations and study the numerical stability of the method in case of a nonlinear advection–diffusion Lotka–Volterra model. The classical numerical methods might be unsuitable for providing accurate numerical results for advection–diffusion problem in which advection dominates diffusion. An improved numerical scheme is proposed, which can preserve the positivity for arbitrary stepsizes. The convergence, boundedness, existence and uniqueness of the numerical solutions are investigated in paper. A threshold value denoted by R 0 Δ x , is introduced in the stability analysis. It is shown that the numerical semi-trivial equilibrium is locally asymptotically stable if R 0 Δ x < 1 and unstable if R 0 Δ x > 1. Moreover, the limiting behaviors of the threshold value are exhibited. Finally, some numerical simulations are given to confirm the conclusions. [ABSTRACT FROM AUTHOR]

One of the most important characteristics of the photovoltaic (PV) modules is their long lifetime (around 25 years). However, recent investigations have shown that PV modules may suffer significant degradation before that time; that is why the development of diagnostic techniques is important for the customers of PV systems. In this paper two indicators to quantify the degradation of a PV module are presented. Such indicators use the single-diode model to represent a PV module without degradation and combine such information with the experimental measurements to estimate the increase in the series resistance and/or the decrease in the parallel resistance with respect to reference values. The estimation of those variations allows the quantification of the module degradation. Simulation results comparing the proposed indicators with the fill factor (a traditional indicator to quantify the electrical quality of a PV module), and other indicators to estimate the series resistance are presented to illustrate the advantages of the proposed indicators. [ABSTRACT FROM AUTHOR]

Computer viruses present a substantial threat to our daily lives. Traditional models for the propagation of computer viruses primarily concentrate on network structures. In this paper, we take into account the constrained availability of resources in the context of computer virus prevention and control. We introduce a computer virus propagation model based on resource limitations. By examining the stability of both toxic and non-toxic equilibria within the model, we employ Matlab and Python for numerical analysis to simulate various computer virus propagation scenarios. Additionally, we present corresponding defense mechanisms for combatting these viruses. [ABSTRACT FROM AUTHOR]

We study the implementation of a Chebyshev spectral method with forward Euler integrator proposed in Berardi et al.(2023) to investigate a peridynamic nonlocal formulation of Richards' equation. We prove the convergence of the fully-discretization of the model showing the existence and uniqueness of a solution to the weak formulation of the method by using the compactness properties of the approximated solution and exploiting the stability of the numerical scheme. We further support our results through numerical simulations, using initial conditions with different order of smoothness, showing reliability and robustness of the theoretical findings presented in the paper. • Convergence of a spectral method for a peridynamic formulation of Richards' equation. • Existence and uniqueness of the solution by its stability and compactness properties. • Simulations to numerically verify the existence of the weak solution to the model. [ABSTRACT FROM AUTHOR]

In this paper, a model with spatial diffusion and mixed delays is presented to describe the spread of echinococcosis between dogs and livestock. Firstly, the local stability is investigated using the Routh–Hurwitz criterion. Furthermore, when considering time delays as bifurcation parameters, the conditions for the occurrence of Hopf bifurcation are discussed based on the linear approximation of the nonlinear system. Lastly, the fixed-time stability is studied under the implementation of appropriate control measures. Numerical simulations are provided to give a better understanding of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we study the split common fixed point problem for two nonlinear mappings in p -uniformly convex and uniformly smooth Banach spaces. We propose an algorithm which uses dynamic stepsize, it allows to be easily implemented without prior information about operator norm. We further apply our result to solve the split variational inclusion problem, equilibrium problem and convexly constrained linear inverse problem. Moreover, we provide numerical examples to verify efficiency of our algorithm. • Presents an iteration process for splitting problems, with dynamic choosing step size. • Implement the result for solving wide classes of mathematical engineering problems. • Includes nontrivial example with computer simulation to compare our findings with existing ones. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the classical chemostat model where the consumption function of the species, in both cases Monod and Haldane, is perturbed by real random fluctuations. Once the existence and uniqueness of non-negative global solution of the corresponding random systems is ensured, we prove the existence of a deterministic compact attracting set, whence we are able to find conditions to guarantee either the extinction or the persistence of the species, the most important aim in real applications. In addition, we depict several numerical simulations to illustrate the theoretical framework, standing out our contributions, providing the biological interpretation of every result and comparing with similar works in the literature. [ABSTRACT FROM AUTHOR]

We consider the inherent attack tolerance properties of resilient model predictive control (R-MPC) for cyber–physical systems (CPSs) modeled by discrete linear time-invariant (LTI) systems subjected to limited disruptions. In this paper, the relationship between the maximum allowable duration of Denial-of-Service (DoS) attacks, namely attacks that disrupt both sensor to controller (S–C) and controller to actuator (C–A) communication channels, and the upper bound of disturbances is deduced at length. Moreover, to achieve robust recursive feasibility and closed-loop stability of the system, we discuss that MPC with state, control and terminal constraints has a certain degree of inherent attack tolerance concerning the DoS attack duration and parameters like system matrices and the nominal terminal set. Finally, numerical simulation is given to substantiate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

The paper focuses on the asynchronous filter design based on hidden Markovian model for Markovian jump systems with time-delay and external disturbances. Cyber nonlinearities in the communication environment are also considered. To further reduce the network bandwidth usage, an internal dynamic variable is introduced based on the previously extensively studied (static) event-triggered method, which is called dynamic event-triggered approach. The hidden Markovian model is utilized to characterize the asynchronous phenomenon caused by clock signals out of sync between system and filter mode. Then, according to the augmented filtering error system dynamics, some less conservative sufficient conditions are proposed to guarantee the stochastic stability with H ∞ performance. Consecutively, the filter parameter-solving problem is synthesized by a convex optimization problem. Finally, two numerical simulations are presented to demonstrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

The non-ordinary state-based peridynamic (NOSB-PD) method has significant advantages in solving crack propagation problems due to its non-local characteristics, but it also faces problems such as numerical oscillations and boundary effects. In order to solve the above defects, the paper first discusses the NOSB-PD method within the Galerkin framework. After that, the peridynamic differential operator (PDDO) approximation was introduced by extending the calculation of the deformation gradient tensor F in NOSB-PD. Since the zero-order approximations in the PDDO approximation and the reproducing kernel (RK) approximation are identical, the distinctions between the two approximations have been thoroughly analysed. Although the two approximations show the same consistency, only the RK approximation satisfies the integrable condition. Therefore, a RK-PD coupling method is proposed in the paper, and an implicit iterative algorithm suited to the RK-PD method is presented as well. At last, several numerical examples demonstrate that the proposed method does not suffer from numerical oscillations and can be used to solve the three-dimensional crack propagation problems. [ABSTRACT FROM AUTHOR]

The article discusses computer simulations of the carbon substance graphene that use the Japanese paper-cutting technique kirigami to create a stretchy and flexible material that preserves the strength of the original material, with comments from researchers Harold Park and Paul McEuen.

Purpose: The purpose of this paper is to verify results related to losses in the core of a brushless DC prototype motor, obtained using its computer FE models, by experimental tests on manufactured machines. The paper focuses on the comparison of losses in the core of a machine with a classical stator core made of an iron–silicon material (Fe–Si) and a new one made of a modern METGLAS material. Design/methodology/approach: Computer models of the prototype motors were created using FEM. The designed machines were manufactured, and experimental tests were performed. To achieve high frequencies in rotating magnetic fields, motors with a stator to rotor pole ratio of 9/12 were built. Twin rotor approach was applied, as two identical rotors were built along the two geometrically identical stators made of different core materials. Findings: Experimental studies have shown the superiority of the METGLAS material over the classical Fe–Si material. Material parameters were measured directly on the prepared cores as library data used in the simulation may be incorrect due to technological processes during core production, which was also verified. Problems related to twin rotor approach have been identified. Solution to the problem has been suggested. Necessity of 3D FEM modelling was identified. Originality/value: The main source of originality is that METGLAS material used in the prototype machines was developed and manufactured by the authors themselves. Original approach to core parameter evaluation based on simplified methodology has been suggested. Another original part is a simplified methodology applied to loss measurement during no-load test. [ABSTRACT FROM AUTHOR]

This paper applies variational Bayesian to the stochastic system filtering problem for arbitrary measurement disturbances. Considering the system's robustness when confronted with disturbances, we model its dynamics with a random walk model. Afterward, by assuming an inverse-Gamma distribution, the newly introduced covariance is estimated under a variational Bayesian (VB) framework. The proposed filter improves robustness against additive disturbance and degrades automatically into a Kalman filter when without disturbance. Moreover, this filter avoids the labor-intensive process of tuning parameters. A numerical simulation and an on-site vehicle navigation experiment are given to illustrate the effectiveness of the proposed filter. [ABSTRACT FROM AUTHOR]

This paper systematically investigates consensus tracking of linear multi-agent systems with disturbances over directed switching topologies. Both state and output feedback H ∞ controllers are jointly synthesized with the triggering mechanism. First, a state-based event-triggered H ∞ controller design for achieving consensus tracking is carried out, which can result in settling the occurrence of disturbances and the reduction of controller updates as well as averting Zeno behavior. Considering the case that only output information of agent is required, an event-triggered H ∞ output feedback controller is then proposed and sufficient condition for the solvability of consensus tracking problem are also derived. Compared with the existing results, the effects of disturbances on directed switching topologies can be tackled when continuous communication and full-state information of the agent are not needed. Numerical simulation are finally conducted to illustrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

According to Buffon's needle problem, you can approximate the value of π by throwing needles onto arrays of parallel lines and counting the number of needles crossing the lines. However, it is time-consuming to do the experiment in reality (in 1901, Lazzarini threw 3408 needles to approximate the value of π). In this paper, we tried to approximate the value of π from easily-accesible images of fallen leaves. We extended Buffon's needle problem in two ways: instead of a simple needle we considered a complex shape, and instead of a uniform size we considered various sizes. After we confirmed the extension by a computer simulation, we approximated the value of π from the images we took experimentally and we while walking. From the experimentally-taken images (50 leaves/image × 20 images), the value of π was approximated as 3.1569. The approximated value of π using the images we took while walking was 3.5961 (the accuracy was not good because it was calculated from one image). [ABSTRACT FROM AUTHOR]

This paper studies the preparation of quantum gates that enable the realization of maximum entangled states, i.e., Bell states. A series of unitary time-evolution operators are derived to realize the Bell states through the Hadamard and CNOT gates. These operators are decomposed based on the Cartan decomposition method and steered by control laws designed based on the Lyapunov control theorem. The numerical simulations show that by adjusting proper control parameters in the designed Lyapunov-based control laws, the Hadamard and CNOT gates can be faster and better prepared through the decomposed operators, and more stable and accelerated Bell states can be achieved. [ABSTRACT FROM AUTHOR]

In this paper, we propose two state feedback strategies to exponentially stabilize eigenstates for quantum spin- 1 2 systems based on the state feedback designed in Liang et al. (2018)[1] and Wen et al. (2022)[2], respectively. In order to obtain faster state convergence, we improve the state feedback by increasing the real-time state convergence rate, and prove the exponential convergence. On this basis, we present the way of achieving global exponential stabilization of quantum spin- 1 2 systems under the improved state feedback with the help of noise-assisted feedback. Besides, we redesign the division of state space to improve the state convergence rate further, and compare the state convergence rates of all state feedback strategies that can exponentially stabilize eigenstates for quantum spin- 1 2 systems. The effectiveness and the superiority of the improved feedback control are also verified in numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, a stochastic SIRS epidemic model with general incidence rate under regime switching is investigated. First of all, by applying the Markov semigroups theory, we establish sufficient condition R T 0 * > 0 for the densities of the distributions of solution converge in L 1 to an invariant density. Then, we prove the extinction of disease under the condition of R T 0 * < 0. Finally, numerical simulations for two special cases of response function are carried out to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

• The paper is the first batch that tries to inquiry the GPS of the PDIMNNs. Furthermore, unlike the previous literature [11,21,35] , the nonlinear substitution that converts the PDs system to a constant delays system is not used. Because the subsequent pro-cessing of the converted system is complicated, this paper directly performs on the original PDs system. • The paper employs the non-reduced-order method, which r-efrains the double-dimensional problem after reduced-order [3–5,23,24]. In practical applications, the method is more ponderable and si-gnificative for second-order scheme under controller. • In the paper, devise both the feedback controller and the adaptive controller for the first time to achieve the GPS of the PD-IMNNs. The advantages of the two types of controllers are compar-ed through numerical examples and simulations. The mathematical model is closer to reality, and selecting the appropriate controller in application can further reduce control expenses. This article probes into the global polynomial stabilization (GPS) of proportional delayed inertial memristive neural networks (PDIMNNs). Here, ruling out the reduced-order way, discuss the GPS of PDIMNNs under the second-order scheme directly. Firstly, a feedback controller is designed to make the system self-stabilizing. By designing suitable Lyapunov functional with adjustable parameters and combining with inequality techniques, two algebraic criteria are obtained to realize the GPS of the PDIMNNs. Owing to the conservatism caused by the ineluctable inequality scaling, it is worth noting that the controller gains are greater than the actual requirements. To further save control expenses, employing an adaptive controller to make the system stabilized. Finally, three numerical examples which sustain the usability of the obtained theoretical conclusions are shown. [ABSTRACT FROM AUTHOR]

This paper presents the qualitative analysis of a predator–prey model with nonmonotonic functional response and impulsive effects. Different from previous work, by considering two factors of nonmonotonic functional response and impulsive effects, this paper studies the existence and stability of the periodic semi-trivial solution y = 0 first. Then, by constructing an appropriate Poincare map and introducing geometric theory, it is shown that the predator–prey model can exhibit a variety of dynamic phenomena, including orbitally asymptotically stable order-1 periodic solution (O1PS), order-2 periodic solution (O2PS) and globally stable equilibrium point under certain conditions. When there exists an O2PS, its appearance and disappearance as well as the appearance of bifurcation phenomenon are discussed in detail with different selections of the initial value of predator. Finally, numerical simulations illustrate the correctness of the results of the theoretical analysis. The theoretical results presented in this paper can be seen as an advancement to the previous related works. [ABSTRACT FROM AUTHOR]

Chaotic systems are widely used in designing encryption algorithms for their ideal dynamical performances. One-dimensional (1D) chaotic maps have the highest efficiency in implementation and have achieved great attention. However, 1D chaotic maps have a common security weakness, which is that their key space is relatively small. Therefore, in this paper, a cluster of 1D quadratic chaotic maps is proposed according to the topological conjugate theory. The 1D chaotic map has three tunable parameters which have a significant expansion in parameter space than the traditional 1D chaotic maps. The 1D map is proved to be chaotic theoretically since it is topologically conjugated with a logistic chaotic map. An example of a 1D quadratic chaotic map is provided in this paper, and several numerical simulation results indicate that this 1D quadratic map has ideal chaotic characteristics, which are consistent with the theoretical analysis. To verify the effectiveness of this 1D quadratic map, a novel image encryption algorithm is proposed. The security of this image encryption algorithm is completely dependent on the properties of the 1D quadratic map. Security experimental test results show that this image encryption algorithm has a high-security level, and is quite competitive with other chaos-based image encryption algorithms. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to propose a new method for robust simulations of passive heat transfer in two-fluid flows with high volumetric heat capacity contrasts. Design/methodology/approach: This paper implements a prediction–correction scheme to evolve the volumetric heat capacity. In the prediction substep, the volumetric heat capacity is evolved together with the temperature. The bounded downwind version of compressive interface capturing scheme for arbitrary meshes and central difference scheme are used for the spatial discretization of the advection and diffusion terms of the heat transfer equation, respectively. In the correction substep, the volumetric heat capacity is updated in accordance with the interface captured by using a coupled level-set and volume-of-fluid method to capture the interface dynamics precisely. Findings: The proposed method is verified by simulating the advection of a hot droplet with high volumetric heat capacity, a stationary air–water tank with temperature variation between top and bottom walls and heat transfer during wave plunging at Re=108. The test results show that the proposed method is practical and accurate for simulating two-fluid heat transfer problems, especially for those feature high volumetric heat capacity contrasts. Originality/value: To ensure the numerical stability, this paper solves an additional conservative form of volumetric heat capacity equation along with the conservative form of temperature equation by using consistent spatial-discretization and temporal-integration schemes. [ABSTRACT FROM AUTHOR]

Smoothed particle hydrodynamics (SPH) simulations of phase transitions are not accurate because of the decrease in liquid particles at the end of the evaporation phase transition. In this paper, we establish a numerical model of droplet evaporation suitable for SPH by introducing a time fractional-order convection–diffusion equation. This model was used to study the evaporation process of droplets under different environments, and the stationary evaporation of droplets was simulated by combining convection–diffusion equations of different orders to determine the optimal order. The results conformed to the " D 2 Law," confirming the effectiveness and accuracy of our method. The model was then used to study the phase transition process of droplets impacting flat and curved surfaces. Among the tested equations, the 0.1-order convection–diffusion equation had the best correction effect on the evaporation model. This equation improved the accuracy of the calculation and had a good corrective effect for both static evaporation and the evaporation of droplets impacting flat and curved surfaces. [ABSTRACT FROM AUTHOR]

In this paper, the finite-time dynamic event-triggered consensus of second-order multi-agent systems with mismatched disturbances is studied. First, a nonlinear finite-time disturbance observer is designed to estimate the mismatched and matched disturbance of each follower. Second, the nonlinear dynamic integral sliding surface is developed through the mismatched and matched disturbance estimated by the observer. Then, combined with the dynamic event trigger strategy and the designed integral sliding surface, a new distributed control protocol is proposed, ensuring the finite-time consensus of the system. An analysis of Zeno behavior has found that the event-triggered interval has a positive lower bound. Finally, the effectiveness of the proposed control algorithm is verified by numerical simulation. [ABSTRACT FROM AUTHOR]

Time-delay is a universal phenomenon in control systems, which usually leads to instability and poor performance of systems. In this paper, the p th moment asymptotic stability of trivial solutions to uncertain dynamical systems with time-delays is investigated. The concept of the generalized expected value is introduced with its properties based on uncertainty theory. Sufficient conditions for ensuring the stability of uncertain delay systems are derived by Lyapunov direct method. Several illustrative examples with numerical simulations are arranged to demonstrate the effectiveness of the stability results. [ABSTRACT FROM AUTHOR]

In this paper, a stage-structured predator–prey model is considered in a toxic environment, emphasizing on the affect of the toxic substances on growth of the species in presence of time delays. The positivity and boundedness of solutions have been discussed. The analytical and numerical simulations of the proposed model show that the coexistence equilibrium point is stable for low and moderate values of the delay parameter associated with the predator's maturity. Even though there is an interval of the maturation time in which the system exhibits oscillatory behaviour, a longer maturity duration may lead to the extinction of the predator species. The impact of toxicity on the proposed system is also investigated. The stability of the system repeatedly switches as the time delay, related to the changes of toxicity incurred in the adult predator, varies, and finally becomes unstable for a significant value of it. Besides that, the delay related to the prey's toxicity has also led some exciting results. [ABSTRACT FROM AUTHOR]

In this paper, we proposed a new fractional derivative operator in which the generalized cardinal sine function is used as a non-singular analytic kernel. In addition, we provided the corresponding fractional integral operator. We expressed the new fractional derivative and integral operators as sums in terms of the Riemann–Liouville fractional integral operator. Next, we introduced an efficient extension of the new fractional operator that includes integrable singular kernel to overcome the initialization problem for related differential equations. We also proposed a numerical approach for the numerical simulation of IVPs incorporating the proposed extended fractional derivatives. The proposed fractional operators, the developed relations and the presented numerical method are expected to be employed in the field of fractional calculus. [ABSTRACT FROM AUTHOR]

In this paper, an observer with exponential time-varying gain is proposed for a class of nonlinear systems in Takagi–Sugeno form with both continuous-time and aperiodic sampled outputs. The proposed observer consists of two parts: one related to the continuous-time outputs and one related to the discrete outputs. Sufficient conditions involving a tuning parameter and the maximum allowed sampling time are derived in terms of quasi linear matrix inequality with respect to a scalar to ensure asymptotic convergence of the observer on the basis of Lyapunov–Krasovskii functional and H ∞ approach. Numerical simulations are provided to show the benefits of the proposed observer. Some comparisons with the high gain continuous-discrete observer and fuzzy observer with constant gain are provided to illustrate the interest of the proposed scheme. [ABSTRACT FROM AUTHOR]

This paper studies the distributed optimal coordinated control problem for Euler–Lagrange multi-agent systems with connectivity preservation. The aim is to force agents to achieve the optimal solution minimizing the sum of the local objective functions while guaranteeing the connectivity of the communication graph. For practical purposes, the gradient vector of the local objective function is allowed to use only at the real-time generalized position instead of at the auxiliary system state. To make the control parameters independent of the global information and guarantee the fully distributed manner of controller, the adaptive control is introduced to update the coupling weights of the relative states among neighbors. Moreover, to reduce the resource for control updates, the event-driven communication is employed for the updates of both the relative states and the gradient of the connectivity-preserving potential function. Based on the Lyapunov analysis framework, it is proved that agents can converge to the optimal solution with connectivity preservation and Zeno behavior is excluded for the two event-triggering conditions. Finally, the effectiveness of the proposed method is verified by a numerical simulation example. [ABSTRACT FROM AUTHOR]

In this paper, we consider a malicious attack issue against remote state estimation in cyber-physical systems. Due to the limited energy, the sensor adopts an acknowledgment-based (ACK-based) online power schedule to improve the remote state estimation. However, the feedback channel will also increase the risk of being attacked. The malicious attacker has the ability to intercept the ACK information and modify the ACK signals (ACKs) from the remote estimator. It could induce the sensor to make poor decisions while maintaining the observed data packet acceptance rate to keep the attacker undetected. To maximize the estimation error, the attacker will select appropriate attack times so that the sensor makes bad decisions. The optimal attack strategy based on the true ACKs and the corrosion ACKs is analytically proposed. The optimal attack time to modify the ACKs is the time when the sensor's tolerance, i.e., the number of consecutive data packet losses allowed, is about to reach the maximum. In addition, such an optimal attack strategy is independent of the system parameters. Numerical simulations are provided to demonstrate the analytical results. [ABSTRACT FROM AUTHOR]

• We study the problem of the target layer state estimation in multilayer complex dynamical networks by using functional observability. • We analyze the relationship between the minimum number of auxiliary nodes in the functional observer design and interlayer connection probability. • The proposed method can achieve the accurate estimation with less placement of observers and fewer computational costs. In large-scale complex dynamical networks, it is significant to estimate the states of target nodes with only a part of measured nodes. Meanwhile, multilayer complex dynamical networks exist widely in society and engineering. Therefore, it has important theoretic meaning and practical value to study the state estimation of target nodes in multilayer complex dynamical networks with limited node measurements. In this paper, with the measurable state information of a portion of nodes in one layer in the multilayer complex dynamical network, the state estimation of target nodes in other layers is studied. First, we build the model of the multilayer complex dynamical network which includes some target nodes and sensor nodes. Second, auxiliary nodes are selected by using the maximum matching principle in graph theory to construct the augmented node set. Third, we discuss the relationship between the minimum number of auxiliary nodes and interlayer connection probability in the multilayer complex dynamical network. Forth, an appropriate functional state observer is designed with limited number of measured nodes according to a typical model-based algorithm. Finally, numerical simulations are given to demonstrate the accuracy of the proposed method. The proposed method can achieve the accurate estimation with less placement of observers and fewer computational costs in the multilayer complex dynamical network. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the problem of leaderless consensus control for the multiagent systems whose nonlinear dynamics satisfying incremental quadratic constraints. A distributed dynamic consensus protocol, decided by communication among neighboring agents, is presented to render nonlinear agent consensus with appropriate coupling weights. Next, an observer-based distributed protocol is considered to ensure consensus of nonlinear system without knowing full state information. Further, extensions to consensus strategies with nonlinear dynamics for the leader-following fashion are also addressed. By comparison to the traditional nonlinear consensus control methodologies, the proposed approach generalizes the Lipschitz nonlinearity as well as the combined nonlinearity of one-sided Lipschitz condition and quadratic inner-boundness condition towards a more generalized type of nonlinearity, which shows us a less conservative result in the Lyapunov proof. Finally, the numerical simulations for six agents are illustrated to show the feasibility and performance of the proposed control protocol with or without the presence of the observer. [ABSTRACT FROM AUTHOR]

In this paper, the dynamic event-based resilient consensus control of the multiple networked Euler-Lagrangian (E-L) systems under the Denial of Service (DoS) attacks is considered. Compared with linear cyber-physical systems, nonlinear networked E-L systems are more complex and closer to actual mechanical systems. For the situation where the topology is a strongly connected directed topology, a controller based on a dynamic event-trigger mechanism is designed to achieve consensus control for the networked E-L system in the absence of DoS attacks. Sufficient conditions are presented, which can guarantee the closed-loop system be stable. Then the resilient consensus problem of event-based controllers under energy-constrained DoS attacks is analyzed. The conditions related to the duration and frequency of DoS attacks are given. Zeno behavior is proved does not exist in the proposed control scheme. Finally, some numerical simulation results are given for verifying the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we study a flocking behavior that may or not appear for Cucker - Smale model with distributed time delays. For the short range communicated Cucker - Smale model, the flocking condition has strong restrictions on initial data. For this case, we mainly consider the non - flocking behavior. By establishing and appropriately estimating an inequality of the position variance such that the second order space moment is unbounded, we drive a sufficient condition for the non - existence of the asymptotic flocking when the time delays satisfy a suitable smallness assumption. Furthermore, we also provide a sufficient condition of asymptotic flocking. Finally, we present numerical simulations to validate the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the optimal consensus control problem of nonlinear multi-agent systems(MASs) with completely unknown dynamics is considered. The problem is formulated in a differential graphical game approach which can be solved by Hamilton-Jacobi (HJ) equations. The main difficulty in solving the HJ equations lies in the nonlinear coupling between equations. Based on the Adaptive Dynamic Programming (ADP) technique, an VI-PI mixed HDP algorithm is proposed to solve the HJ equations distributedly. With the PI step, a suitable iterative initial value can be obtained according to the initial policies. Then, VI steps are run to get the optimal solution with exponential convergence rate. Neural networks (NNs) are applied to approximate the value functions, which makes the data-driven end-to-end learning possible. A numerical simulation is conducted to show the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper focuses on the distributed observer design problem of a discrete-time complex dynamical system with long-rang interactions, where the outputs of the system are measured by a group of agents communicating through a directed graph and each agent can access only a part of ones. By introducing the variant d -path Laplacian matrix to describe the long-rang interactions among the multiple agents, a simple full-order distributed observer is first designed. Then, in order to reduce to the number of integrators in the distributed observer, a reduced-order distributed observer is constructed. Finally, some numerical simulations are presented to verify the theoretical results. [ABSTRACT FROM AUTHOR]

This paper presents a theoretical and numerical investigation of stationary and oscillatory patterns in a spatial model of bacteria quiescence. The reaction–diffusion model consists of active and inactive microbial populations in a harsh environment accounting for the directed movement and switch of cells to dormancy at high concentration levels. We present a bifurcation analysis of the model and the interplay between Turing and Hopf instability is discussed. Numerical simulations supporting the existence of spatially homogeneous solutions, as well as stable spatial patterns and oscillatory patterns are presented. [ABSTRACT FROM AUTHOR]

Various types of heat exchangers have many applications in industrial and engineering fields to improve heat transfer rate (HTR). The techniques of heat transfer enhancement which are active, passive, and hybrid are discussed in the present review paper. One of passive methods to enhance HTR is the use of nanofluids. This article provides the governing equations of nanofluid flows and discusses their modeling methods, including single-phase and two-phase. Advanced investigations considered single-phase and two-phase flow regimes are summarized. Comparing single-phase models (SPMs) and two-phase models (TPMs), most researchers concluded that numerical modeling based on TPMs experiences a better prediction compared to the SPMs. However, there are conflicting results among the researchers and it is not confirmed which model is better. This review paper aims to analyze the examinations on SPMs and TPMs in heat exchangers to assess the impact of these approaches on the prediction of the characteristics of nanofluids in these devices. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this study is to investigate the effects of the shear-thinning viscoelastic behavior of the surrounding matrix on droplet deformation by weakly compressible smoothed particle hydrodynamics (WC-SPH). Also, the effect of the presence of another droplet is examined. Design/methodology/approach: A modified consistent weakly compressible SPH method is proposed. After code verification, a complete parameter study is performed for a drop under the simple shear flow of a Giesekus liquid. The investigated parameters are 0.048≤Ca ≤ 14.4, 0.1≤c ≤ 10, 0.04≤De ≤ 10, 0≤α ≤ 1 and 0.12≤Re ≤ 12. Findings: It is demonstrated that the rheological behavior of the surrounding fluid could dramatically affect the droplet deformation. It is shown that the droplet deformation is increased by increasing Re and Ca. In contrast, the droplet deformation is decreased by increasing a, De and polymer content. Also, it is indicated the presence of another droplet could drastically affect the flow field, and the primary stress difference (N1) is resonated between two droplets. Originality/value: The main originality of this paper is to introduce a new consistent WC-SPH algorithm. The proposed method is very versatile for tackling the shear-thinning viscoelastic multiphase problems. Furthermore, a complete parameter study is performed for a drop under the simple shear flow of Giesekus liquid. Another novelty of the current paper is studying the effect of the presence of a second droplet. To the best of the authors' knowledge, this is performed for the first time. [ABSTRACT FROM AUTHOR]

Anti-disturbance state estimation for reaction–diffusion neural networks (RDNNs) subject to persistent dwell-time (PDT) switching constraints is investigated in this paper. First, PDT switching that can be utilized to characterize both the fast and slow switching processes is used in this paper to accurately model the RDNNs. Moreover, by designing the time-sampling and space-splitting measurement algorithms, the proposed state estimator can significantly reduce the measurement cost while tolerating the frequent asynchrony of the system modes and estimator ones caused by the sensor update lag. Furthermore, a state estimator is constructed to obtain the state of RDNNs affected by matched disturbances. To suppress the impact of the disturbance on the system's state estimation, a disturbance observer and a disturbance-related controller are designed to estimate the disturbance information and ensure state estimation performance. Then, sufficient conditions for the proposed state estimator making the estimation error bounded are derived. Finally, numerical simulations for switched RDNNs with two-dimensional spatial diffusion are presented to illustrate the effectiveness and superiority of the proposed method. • Different from existing 1D spatial switched RDNNs, this paper focuses on switched RDNNs with high-dimensional diffusion and PDT switching rule, which are more in line with the system characteristics. • A combined time-sampling and space-splitting measurement method is proposed to reduce the measurement cost. To address the frequent asynchrony of system modes and estimator ones, stability analysis and estimator design are performed using iterative and recursive methods. • To obtain the system's state and to minimize the effect of disturbances on state estimation, an anti-disturbance state estimation scheme is proposed for PDT-switched RDNNs based on the disturbance observer. [ABSTRACT FROM AUTHOR]

This paper focuses on the p th moment exponentially stability for Markov switching and multi-impulse jumps stochastic time-varying delay system, where the switching behavior among subsystems of the target system is determined by Markov chains, and the occurrence of impulsive jumps is decided according to event-triggered impulsive mechanism when certain well-designed conditions are satisfied. By applying the Itô formula, Gronwall inequality and Razumikhin theorem, some novel sufficient criteria are provided to assure the system stability and get rid of Zeno phenomenon. It is worth pointing out that the multi-impulse jumps are our research aim and the range of delays considered is relatively wide, i.e., the daily bounded delay τ (t) ∈ [ 0 , 1) and the unupper bound delay τ (t) ∈ [ 1 , ∞). Subsequently, two diverse event trigger mechanism about impulsive jumps are proposed for such two types of delays, namely the defined event-triggered impulsive mechanism with delay. Finally, the validity and feasibility of the developed theoretical results are verified by two numerical simulations. • Different from the bounded delay system in Wang et al. (2023), Peng et al. (2021),Li and Zhu (2023),Peng et al. (2010), Zhu (2014), Zhua and Cao (2012),Yang and Zhu (2014), Xu and Zhu (2022), we discuss the daily bounded delay τ (t) ∈ [ 0 , 1) and the unupper bound delay τ (t) ∈ [ 1 , ∞). Two categories of event trigger impulsive method named event-triggered impulsive mechanism with delay (ETIMD) are proposed for two types delay, respectively. And in event-triggered condition, it fully consider the impact of delays. Moreover, the upper bound of the delay τ (t) ∈ [ 0 , 1) is required to avoid Zeno phenomenon. While for τ (t) ∈ [ 1 , ∞) , only the lower bound is required to escape Zeno phenomenon, in which is independent of the delayed upper bound. • Compared with Wang et al. (2022), Li et al. (2020), Peng et al. (2021), Zhu (2014), Xu and Zhu (2022), the Markov switching and multi-impulse jumps stochastic time-varying delay system as a benchmark is considered in this paper, where the switching behavior between subsystems is driven by Markov chains, and the occurrence of impulsive jump is decided according to ETIMD strategy. It should be emphasized that the multi-impulse jumps are the research goal. Thus, the system in [27,28,36,43] could be regarded as a special case of the stochastic delay system when the Markov switching is not considered in this study. • By applying the Itô formula, Gronwall inequality and Razumikhin theorem, some novel sufficient criteria of Lyapunov-Razumikhin type for p-ES are provided for unstable subsystems with stable impulses. [ABSTRACT FROM AUTHOR]

The identification problem of output-error autoregressive (OEAR) systems with scarce measurements is considered in this paper. In order to overcome the massive absence of outputs, an interval-varying recursive identification algorithm is proposed through changing the sampling interval and skipping the missing outputs. Based on the maximum likelihood principle, a maximum likelihood interval-varying recursive least squares algorithm is proposed. The effectiveness of the proposed algorithm is tested by a numerical simulation example, and an application example about the heading motion control of underwater vehicle. [ABSTRACT FROM AUTHOR]

Prey-taxis, which plays an important role in biological control and ecological balance, is the phenomenon that predators shift directly toward regions with the highest density of prey. In this paper, we consider a spatiotemporal predator–prey system involving prey-taxis and nonconstant mortality. By structuring Lyapunov functional, we obtain the global stability of spatially homogeneous steady states. The minimal mortality of predator will determine whether they can survive. In addition, we identify the parameter ranges that spatially homogeneous steady state remains stable or becomes unstable, and discuss steady state bifurcation by choosing prey-taxis coefficient. It is found that a diffusion-induced instability can occur under nonconstant mortality, and prey-taxis can annihilate the spatial patterns induced by diffusion. Numerical simulations illustrate that prey-taxis and nonconstant mortality can result in rich pattern formations including spots pattern, spots–strips pattern, labyrinth pattern, strips-like pattern. It is worth noting that the weak prey-taxis is disadvantageous in terms of the number of two species. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to discuss a new form of the Adomian decomposition technique for the numerical treatment of Bratu's type one-dimensional boundary value problems (BVPs). Moreover, the author also addresses convergence and error analysis for the completeness of the proposed technique. Design/methodology/approach: First, the author discusses the standard Adomian decomposition method and an algorithm based on Duan's corollary and Rach's rule for the fast calculation of the Adomian polynomials. Then, a new form of the Adomian decomposition technique is present for the numerical simulation of Bratu's BVPs. Findings: The reliability and validity of the proposed technique are examined by calculating the absolute errors of Bratu's problem for some different values of Bratu parameter λ. Numerical simulation demonstrates that the proposed technique yields higher accuracy than the Bessel collocation and other known methods. Originality/value: Unlike the other methods, the proposed technique does not need linearization, discretization or perturbation to handle the non-linear problems. So, the results obtained by the present technique are more physically realistic. [ABSTRACT FROM AUTHOR]

A complex dynamical network (CDN) can be considered as the composition system with the nodes subsystem (NS) and the links subsystem (LS), and both subsystems are coupled with each other. Therefore, the dynamics of NS affects the dynamics of LS, and vice versa. In this paper, two vector differential equation (VDE)s are employed to describe the dynamics of NS and LS, respectively, in which the dynamics of NS is proposed as the VDE with the second derivative term (SDT) for more realistic engineering applications. Compared with the existing literature, the key advantage is that the dynamics of links is utilized to assist synthesizing the tracking controller of NS. The results show that when the state of LS tracks asymptotically the synthesized auxiliary tracking goal (ATG), the state of NS tracks asymptotically the given reference signal. Observing the eventual topology of CDN, all eventual links between nodes depend on the proposed ATG when NS achieving the tracking target, in which one special case is that if all target signals determined by ATG are not zero, all nodes are not isolated. Finally, the effectiveness of the proposed control scheme is verified by a numerical simulation example. [ABSTRACT FROM AUTHOR]

In this paper, the mean-square exponential synchronization of stochastic multilayer networks with white-noise-based time-varying coupling is investigated via intermittent dynamic periodic event-triggered control. The existence of a dynamic term can reduce the number of event triggers. Furthermore, by introducing periodic sampling mechanism, a minimum inter-execution time is guaranteed to avoid Zeno phenomenon. Additionally, by employing Lyapunov method, graph theory, and stochastic analysis techniques, synchronization criteria for multilayer networks under intermittent dynamic periodic event-triggered control are established. To clarify the process of synchronization of multilayer networks, a brief framework is developed on the basis of Tajan's algorithm. Ultimately, theoretical results are applied into Chua's circuits and corresponding numerical simulations are given to illustrate the effectiveness and feasibility of the results. [ABSTRACT FROM AUTHOR]

In this paper, an event-triggered joint adaptive high-gain observer design method is proposed for a class of nonlinear systems that are characterized by an unknown parameter entering the system state equations. The main difficulty in the observer design is that the event-triggered mechanism (ETM) is affected by variable delayed-sampled data and the system's unknown parameter. To overcome this difficulty, a closed-loop output predictor is incorporated into the design of the event-triggered mechanism to compensate for the sampling and the delay affecting the system outputs. To prevent the Zeno phenomenon, and to guarantee the exponential convergence of the observer, an exponential decay factor is considered in the ETM. The effectiveness of our proposed observer is demonstrated through numerical simulations, experiments and performances comparison with previous works in the literature. [ABSTRACT FROM AUTHOR]