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In this paper, a new delayed fractional-order model including susceptible migratory birds, infected migratory birds and predators is proposed to discuss the spread of diseases among migratory birds. Fear of predators is considered in the model, as fear can reduce the reproduction rate and disease transmission rate among prey. First, some basic mathematical results of the proposed model are discussed. Then, time delay is regarded as a bifurcation parameter, and the delay-induced bifurcation conditions for such an uncontrolled system are established. A novel periodic pulse feedback controller is proposed to suppress the bifurcation phenomenon. It is found that the control scheme can successfully suppress the bifurcation behavior of the system, and the pulse width can be arbitrarily selected on the premise of ensuring the control effect. Compared with the traditional time-delay feedback controller, the control scheme proposed in this paper has more advantages in practical application, which not only embodies the advantages of low control cost and easy operation but also caters to the periodic changes of the environment. The proposed control scheme, in particular, remains effective even after the system has been disrupted by a constant. Numerical simulation verifies the correctness of the theoretical results. [ABSTRACT FROM AUTHOR]

Time series forecasting has played an important role in different industries, including economics, energy, weather, and healthcare. RNN-based methods have shown promising potential due to their strong ability to model the interaction of time and variables. However, they are prone to gradient issues like gradient explosion and vanishing gradients. And the prediction accuracy is not high. To address the above issues, this paper proposes a Fractional-order Lipschitz Recurrent Neural Network with a Frequency-domain Gated Attention mechanism (FLRNN-FGA). There are three major components: the Fractional-order Lipschitz Recurrent Neural Network (FLRNN), frequency module, and gated attention mechanism. In the FLRNN, fractional-order integration is employed to describe the dynamic systems accurately. It can capture long-term dependencies and improve prediction accuracy. Lipschitz weight matrices are applied to alleviate the gradient issues. In the frequency module, temporal data are transformed into the frequency domain by Fourier transform. Frequency domain processing can reduce the computational complexity of the model. In the gated attention mechanism, the gated structure can regulate attention information transmission to reduce the number of model parameters. Extensive experimental results on five real-world benchmark datasets demonstrate the effectiveness of FLRNN-FGA compared with the state-of-the-art methods. [ABSTRACT FROM AUTHOR]

This paper explored the finite-time stability (FTS) of fractional-order fuzzy inertial neural network with mixed delays. First, the dimension of the model was reduced by the order reduction method. Second, by leveraging the fractional-order finite-time stability theorem, fractional calculus and inequality methods, we established some sufficient conditions to guarantee the FTS of the model under feasible delay-dependent feedback controller and delay-dependent adaptive controller, respectively. Additionally, we derived the settling times (STs) for each control strategy. Finally, we provided two examples to substantiate our findings. [ABSTRACT FROM AUTHOR]

This paper is primarily dedicated to investigating the existence of solutions for an impulsive fractional neutral pantograph integro-differential system (IFNPIDS) through the utilization of the Caputo-Fabrizio (CF) operator. We introduce a novel solution for our addressing system and employ fixed-point techniques to establish innovative results. The paper concludes by presenting two numerical examples, illustrating the practical applicability of our theoretical findings. [ABSTRACT FROM AUTHOR]

As one promising solution, zero-watermarking approaches have been proposed to enhance the image visual quality and applied to protect the intellectual property rights of the medical images, remote sensing images and military images. The moments and their invariants have good image descriptive capability and geometrical invariance, which are common tools for image zero-watermarking. However, there are still some problems. Firstly, most of the existing algorithms ignore the problem of balancing robustness and discriminability. Secondly, the direct computation of image moments is time-consuming, numerically inaccurate, and unstable, thus affecting the effectiveness of these moment-based methods. Third, there is less research on zero-watermarking algorithms targeted at color images. To address these problems, this paper presents a zero-watermarking algorithm which is based on accurate quaternion fractional-order pseudo-Jacobi–Fourier moments with time–frequency analysis capability for color images. Firstly, we define a new set of orthogonal moments, named fractional-order pseudo-Jacobi–Fourier moments (FPJFMs), which is characterized by the generic nature and time–frequency analysis capability. And, we propose a scheme for the accurate computation of FPJFMs. Also, we extend accurate FPJFMs to the accurate quaternion FPJFMs (QFPJFMs), which is an efficient color image representation. Next, a new framework is proposed, namely hybrid low-order moment feature (HLMF) based on accurate QFPJFMs, which can simultaneously improve the legibility and robustness of the image representation. Finally, the accurate QFPJFMs-based HLMF is adapted to the zero-watermarking algorithm. Numerous experiment results indicate that this paper's presented zero-watermarking approach provides a good balance between robustness and discriminability, which is an effective and superior scheme. [ABSTRACT FROM AUTHOR]

Metaheuristic optimization algorithms (MHA) play a significant role in obtaining the best (optimal) values of the system's parameters to improve its performance. This role is significantly apparent when dealing with systems where the classical analytical methods fail. Fractional-order (FO) systems have not yet shown an easy procedure to deal with the determination of their optimal parameters through traditional methods. In this paper, a recent, systematic. And comprehensive review is presented to highlight the role of MHA in obtaining the best set of gains and orders for FO controllers. The systematic review starts by exploring the most relevant publications related to the MHA and the FO controllers. The study is focused on the most popular controllers such as the FO-PI, FO-PID, FO Type-1 fuzzy-PID, and FO Type-2 fuzzy-PID. The time domain is restricted in the articles published through the last decade (2014:2023) in the most reputed databases such as Scopus, Web of Science, Science Direct, and Google Scholar. The identified number of papers, from the entire databases, has reached 850 articles. A Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) methodology was applied to the initial set of articles to be screened and filtered to end up with a final list that contains 82 articles. Then, a thorough and comprehensive study was applied to the final list. The results showed that Particle Swarm Optimization (PSO) is the most attractive optimizer to the researchers to be used in the optimal parameters identification of the FO controllers as it attains about 25% of the published papers. In addition, the papers that used PSO as an optimizer have gained a high citation number despite the fact that the Chaotic Atom Search Optimization (ChASO) is the highest one, but it is used only once. Furthermore, the Integral of the Time-Weighted Absolute Error (ITAE) is the best nominated cost function. Based on our comprehensive literature review, this appears to be the first review paper that systematically and comprehensively addresses the optimization of the parameters of the fractional-order PI, PID, Type-1, and Type-2 fuzzy controllers with the use of MHAs. Therefore, the work in this paper can be used as a guide for researchers who are interested in working in this field. [ABSTRACT FROM AUTHOR]

This paper investigates the attitude control of rigid spacecraft in the presence of uncertainties, disturbances, and actuator faults. In order to effectively address these challenges and improve the performance of the system, a novel actor-critic neural-network-based fractional-order sliding mode control (ACNNFOSMC) has been developed for spacecraft. The integration of actor-critic neural network, fractional-order theory, and sliding mode control enables dual functionality: the actor-critic neural network serves to approximate the aggregate of uncertain parameters, disturbances, and actuator faults, thereby facilitating their compensation, while the fractional-order sliding mode control mechanism significantly improves the system's tracking precision and overall robustness against uncertainties. Theoretical analyses are presented to analyze the stability of the proposed control framework. Thorough examination via simulation experiments affirms the effectiveness and control precision of attitude of our proposed control strategy, even in complex operational scenarios. [ABSTRACT FROM AUTHOR]

This paper focuses on the influence of the fractional-order (FO) resonant capacitor on the zero-voltage-switching quasi-resonant converter (ZVS QRC). The FO impedance model of the capacitor is introduced to the circuit model of the ZVS QRC; hence, a piecewise smooth FO model is developed for the converter. Numerical solutions of the converter are obtained by using both the fractional Adams–Bashforth–Moulton (F-ABM) method and Oustaloup's rational approximation method. In addition, the analytical solution of the converter is obtained by the Grünwald–Letnikov (GL) definition, which reveals the influence of the FO resonant capacitor on the zero-crossing point (ZCP) and resonant state of the converter. An experimental platform was built to verify the results of the theoretical analysis and numerical calculation. [ABSTRACT FROM AUTHOR]

In this paper, the dynamical behaviors of a discrete-time fractional-order population model are considered. The stability analysis and the topological classification of the model at the fixed point have been investigated. It is shown that the model undergoes flip and Neimark–Sacker bifurcations around the co-existence fixed point by using the bifurcation and the normal form theory. These bifurcations lead to chaos when the parameter changes at critical point. In order to control chaotic behavior in the model result from Neimark–Sacker bifurcation, the OGY feedback method has been used. Furthermore, some numerical simulations, including bifurcation diagrams, phase portraits and maximum Lyapunov exponents of the presented model are plotted to support the correctness of the analytical results. The positive Lyapunov exponents demonstrate that chaotic behavior exists in the considered model. [ABSTRACT FROM AUTHOR]

This paper shows solicitude for the generalized projective synchronization of Caputo fractional-order uncertain memristive neural networks (FOUMNNs) with multiple delays. By extending the constant scale factor to the time-varying function matrix, we establish an extraordinary synchronization mode called time-varying function matrix projection synchronization (TFMPS), which is a generalized version of traditional matrix projection synchronization, modified projection synchronization, complete synchronization, and anti-synchronization. To achieve the goal of TFMPS, we design a novel mixed controller including the open loop feedback control and impulsive control, which employs the state information in the time-delayed interval and the sampling information at the impulse instants. It has a prominent advantage that impulse intervals are not restricted by time delays. To establish the connection between the error system and the auxiliary system, a generalized fractional-order comparison theorem with time-varying coefficients and impulses is established. Applying the stability theory, the comparison theorem, and the Laplace transform, new synchronization criteria of FOUMNNs are acquired under the mixed impulsive control schemes, and the derived synchronization theorem and corollary can effectively expand the correlative synchronization achievements of fractional-order systems. [ABSTRACT FROM AUTHOR]

In this paper, we ponder a kind of discrete-time fractional-order complex-valued fuzzy BAM neural network. Firstly, in order to guarantee the quasi-projective synchronization of the considered networks, an original quantitative control strategy is designed. Next, by virtue of the relevant definitions and properties of the Mittag-Leffler function, we propose a novel discrete-time fractional-order Halanay inequality, which is more efficient for disposing of the discrete-time fractional-order models with time delays. Then, based on the new lemma, fractional-order h-difference theory, and comparison principle, we obtain some easy-to-verify synchronization criteria in terms of algebraic inequalities. Finally, numerical simulations are provided to check the accuracy of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

Modern social networks are especially beneficial for spreading rumors since they perform as multichannel communication platforms. The spread of false information has a detrimental impact on people, communities, and businesses. Media reports significantly affect rumor propagation by providing inhibiting factors. In this paper, we propose a new ISCRM fractional-order model to analyze the law of rumor propagation and provide appropriate control strategies. First, under fractional differential equations, the boundedness and non-negativeness of the solutions are obtained. Second, the local and global asymptotic stability of the rumor-free equilibrium and rumor-permanence equilibrium are proved. Third, employing Pontryagin's maximum principle, the conditions necessary for fractional optimum control are derived for the rumor model, and the optimal solutions are analyzed. Finally, several numerical simulations are presented to verify the accuracy of the theoretical results. For instance, while media reports can mitigate the propagation of rumors across various dynamic regions, they are unable to completely restrain rumor spread. [ABSTRACT FROM AUTHOR]

This paper investigates the global Mittag-Leffler stability of memristor-based fractional-order neural networks with mixed time-delay and impulsive. Firstly, based on assumptions, we get a Lemma about distributed delay, which is used to deal with the problems in this paper. Secondly, with the help of contraction mapping principle, the existence and uniqueness of the solution of the system are proved in this paper. Finally, this paper obtains a new sufficient condition which ensures the system globally Mittag-Leffler stable. Numerical simulations are used to verify the correctness and validity of the results in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we study the quasi-synchronization control for a class of fractional-order quaternion-valued neural networks (QVNNs). Unlike previous studies, the introduce of the reaction–diffusion terms makes the model more comprehensive. It is worth mentioning that in earlier literature, there are rare results based on linear matrix inequality method when using the decomposition method (dividing the system into four real-valued ones) to study the synchronization for QVNNs, which is due to the great challenge posed by the cross-product terms. In this work, we overcome this problem by processing the cross-product term as some free variables and then obtain the quasi-synchronization criterion of the system by linear matrix inequalities (LMI) method, which extends some previous works. Finally, a numerical example is given to support the results of this paper. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of bifurcation analysis and bifurcation control of a fractional-order gene regulatory network with sRNA. Firstly, the process of stability change of system equilibrium under the influence of the sum of time delay is discussed, the critical condition of Hopf bifurcation is explored, and the effect of fractional order on the system stability domain. Secondly, aiming at the system's instability caused by a large time delay, we design a controller to improve the system's stability and derive the parameter conditions that satisfy the system's stability. It is found that changing the parameter values of the controller within a certain range can control the system's nonlinear behaviours and effectively expand the stability range. Then, a numerical example is given to illustrate the results of this paper. [ABSTRACT FROM AUTHOR]

At present, stochastic resonance (SR) based on Duffing and Langevin equations has been widely studied, but there is little research on SR phenomenon in higher-dimensional fractional-order systems. Based on the fractional-order Lorenz-like system, the SR phenomenon is studied from the perspective of equilibrium point in this paper. The dynamic process of SR phenomenon is presented, and several key parameters are derived. The results of numerical simulation show that the boundary of SR and chaos system will be broken if the order of the fractional-order system or internal parameters is properly adjusted, and the effect of SR phenomenon will also be influenced. This paper connects two important nonlinear phenomena (chaos and SR) based on the fractional-order system, which provides a new idea for the conversion between chaos and SR systems. [ABSTRACT FROM AUTHOR]

This paper investigates the global synchronization problems of fractional-order complex dynamical networks with uncertain inner coupling and multiple time delays. In particular, both internal time delays and coupling time delays are introduced into our model. To overcome the difficulties caused by various delays and uncertainties, a generalized delayed comparison principle with fractionalorder and impulsive effects is established by using the Laplace transform. Based on the Lyapunov stability theory and mixed impulsive control technologies, some new synchronization criteria for concerned complex dynamical networks are derived. In addition, the synchronization criteria are related to the impulsive interval, network topology structure, fractional-order, and control gains. The theoretical results obtained in this paper can enhance the value of previous related works. Finally, numerical simulations are presented to show the correctness of our main results. [ABSTRACT FROM AUTHOR]

This paper concerns an improved model-free adaptive fractional-order control with a high-order pseudo-partial derivative for uncertain discrete-time nonlinear systems. Firstly, a new equivalent model is obtained by employing the Grünwald–Letnikov (G-L) fractional-order difference of the input in a compact-form dynamic linearization. Then, the pseudo-partial derivative (PPD) is derived using a high-order estimation algorithm, which provides more PPD information than the previous time. A discrete-time model-free adaptive fractional-order controller is proposed, which utilizes more past input–output data information. The ultimate uniform boundedness of the tracking errors are demonstrated through formal analysis. Finally, the simulation results demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Car-like mobile robots (CLMRs) are extensively utilized in various intricate scenarios owing to their exceptional maneuverability, stability, and adaptability, in which path planning is an important technical basis for their autonomous navigation. However, path planning methods are prone to inefficiently generate unsmooth paths in narrow and large-size scenes, especially considering the chassis model complexity of CLMRs with suspension. To this end, instead of traditional path planning based on an integer order model, this paper proposes fractional-order enhanced path planning using an improved Ant Colony Optimization (ACO) for CLMRs with suspension, which can obtain smooth and efficient paths in narrow and large-size scenes. On one hand, to improve the accuracy of the kinematic model construction of CLMRs with suspension, an accurate fractional-order-based kinematic modelling method is proposed, which considers the dynamic adjustment of the angle constraints. On the other hand, an improved ACO-based path planning method using fractional-order models is introduced by adopting a global multifactorial heuristic function with dynamic angle constraints, adaptive pheromone adjustment, and fractional-order state-transfer models, which avoids easily falling into a local optimum and unsmooth problem in a narrow space while increasing the search speed and success rate in large-scale scenes. Finally, the proposed method's effectiveness is validated in both large-scale and narrow scenes, confirming its capability to handle various challenging scenarios. [ABSTRACT FROM AUTHOR]

In this paper, our primary goal is to investigate the existence of solutions for an impulsive fractional integro-differential system (IFIDS) subject to boundary value conditions (BVC), utilizing the Caputo-Fabrizio operator (CFO). Through the application of fixed-point methodologies, we derive original insights into the existence of solutions. The final section of the study incorporates three numerical examples, serving to illustrate the practical application of the theoretical concepts introduced. [ABSTRACT FROM AUTHOR]

This paper examines the boundary stabilisation results for time fractional-order reaction-diffusion systems involving with time-varying delays. The main goal is to design the boundary control for the system by proving the well-posedness of the kernel function using the backstepping method. An invertible Volterra integral transformation is used to convert the considered system into a stable target system. Different from the existing results, the stability results for fractional RDEs are discussed in the sense of the Lyapunov–Krasovskii theory and sufficient conditions are derived with the help of the linear matrix inequality (LMI) approach. Finally, to show the application of the results, the proposed conditions are numerically validated over a time fractional-order reaction-diffusion cellular neural network model. [ABSTRACT FROM AUTHOR]

This paper focuses on establishing the existence results for a coupled implicit impulsive fractional differential system (CIIFDS) utilizing the Caputo-Fabrizio (CF) operator. Employing fixedpoint approaches within generalized metric spaces (GMS), we derive novel findings regarding the existence of solutions. To illustrate the practical application of the presented theoretical concepts, a numerical example is provided in the concluding part of the investigation. [ABSTRACT FROM AUTHOR]

Controllability is a fundamental issue in the field of fractional complex network control, yet it has not received adequate attention in the past. This paper is dedicated to exploring the controllability of complex networks involving the Caputo fractional derivative. By utilizing the Cayley–Hamilton theorem and Laplace transformation, a concise proof is given to determine the controllability of linear fractional complex networks. Subsequently, leveraging the Schauder Fixed-Point theorem, controllability Gramian matrix, and fractional calculus theory, we derive controllability conditions for nonlinear fractional complex networks with a weighted adjacency matrix and Laplacian matrix, respectively. Finally, a numerical method for the controllability of fractional complex networks is obtained using Matlab (2021a)/Simulink (2021a). Three examples are provided to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

In the paper, a backstepping control strategy based on a fractional-order finite-time command filter and a fractional-order finite-time disturbance observer is proposed for the trajectory tracking control of an unmanned surface vehicle. A fractional-order finite-time command filter is presented to estimate the derivatives of the intermediate control, which cannot be directly calculated, thereby reducing the chattering generated by the integer-order command filter. The fractional-order finite-time disturbance observer is presented to approximate and compensate for the model uncertainty and unknown external disturbances in the system. Subsequently, the globally asymptotically stable nature of the closed-loop system is proved based on the Lyapunov method. The effectiveness of the method is proven by simulation experiments on unmanned surface vehicles. [ABSTRACT FROM AUTHOR]

In this paper, we aim to establish the uniform stability criteria for fractional‐order time‐delayed gene regulatory networks with leakage delays (FOTDGRNL). First, we establish the existence and uniqueness of the considered systems by using the Banach fixed point theorem. Second, the delay‐dependent uniform stability and robust uniform stability of FOFGRNLT are investigated with the help of certain analysis techniques depending on equivalent norm techniques. Finally, the paper comes up with two numerical examples to justify the applicability of our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, a new fractional-order seed chaotic generator is designed to solve the problem of the complex operations of single low-dimensional systems and simple high-dimensional systems. The fractional-order chaotic system generated is proven to have better chaotic performance using Lyapunov exponential differential calculus, approximate entropy, 0–1 test and other indicators. On this basis, the "multiple squares nested body scrambling (MSNBS)" model is extended from fractal theory to complete the image scrambling process, and a new algorithm is proposed to be applied to the encryption field in combination with the fractional-order coupled chaotic system. Experimental simulations show that the algorithm can resist common differential attacks and noise attacks and improve the security of the algorithm. [ABSTRACT FROM AUTHOR]

Various scholars have lately employed a wide range of strategies to resolve specific types of symmetrical fractional differential equations. This paper introduces a new implicit finite difference method with variable-order time-fractional Caputo derivative to solve semi-linear initial boundary value problems. Despite its extensive use in other areas, fractional calculus has only recently been applied to physics. This paper aims to find a solution for the fractional diffusion equation using an implicit finite difference scheme, and the results are displayed graphically using MATLAB and the Fourier technique to assess stability. The findings show the unconditional stability of the implicit time-fractional finite difference method. This method employs a variable-order fractional derivative of time, enabling greater flexibility and the ability to tackle more complicated problems. [ABSTRACT FROM AUTHOR]

This paper deals with a class of fractional-order octonion-valued neural networks (FOOVNNs) with impulsive effects. Firstly, although the multiplication of octonion numbers does not satisfy the commutativity and associativity, we don't need to separate an octonion-valued system into eight real-valued systems. Secondly, by applying the appropriate Lyapunov function, and inequality techniques, we obtain the global asymptotical synchronization of FOOVNNs. Finally, we give two illustrative examples to illustrate the feasibility of the proposed method. [ABSTRACT FROM AUTHOR]

This paper introduces the finite-time passivity (FTP) issue of the fractional-order delayed quaternion-valued neural networks (FOQVNNs). The notions of FTP, finite-time input strict passivity (FTISP), and finite-time output strict passivity (FTOSP) of FOQVNNs are presented on the groud of the existing definitions of FTP of fractional-order neural networks. Then, sufficient criteria to guarantee the FTP (FTISP, FTOSP) of the system are developed utilizing the given definitions, Lyapunov function theory, inequality technique, and an appropriate controller is established. Additionally, the presented finite-time stability criterion and setting-time are according to the concept of FTP. At last, the significance of the theoretical results are tested by a simulation experiment. [ABSTRACT FROM AUTHOR]

This research paper presents an eco-epidemiological model that investigates the intricate dynamics of a predator–prey system, considering the impact of fear-induced stress, hunting cooperation, global warming, and memory effects on species interactions. The model employs fractional-order derivatives to account for temporal dependencies and memory in ecological processes. By incorporating these factors, we aim to provide a more comprehensive understanding of the underlying mechanisms that govern the stability and behavior of ecological systems. Mathematically we investigate system's existence, equilibria and their stability. Moreover, global stability and hopf bifurcation also analyzed in this study. Numerical simulations have been performed to validate the analytical results. We find that the coexistence equilibrium is stable under specific conditions, along with the predator equilibrium and the disease-free equilibrium. Bifurcation analyses demonstrate the intricate behavior of species densities in response to changes in model parameters. Fear and global warming are found to stabilize the system, while cooperation and additional food for predators lead to destabilization. Additionally, the influence of species memory has been explored. We observe that memory tends to stabilize the system as species memory levels increase. [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]

This paper presents a novel control strategy based on an uncertainty estimator for a class of fractional-order nonlinear systems characterized by a polynomial input. The proposed strategy allows the system to be controlled without resorting to transformations or approximate linearization. This is accomplished by using a fractional-order sliding-mode observer, whose task is to estimate certain portions of the state of the nonlinear system of a non-integer order, thus allowing the control law to counteract these elements to steer the system towards a desired behavior. To validate the performance of the proposed strategy, it was implemented, both in simulation and experimentally, to regulate the temperature of the cold side of a thermoelectric module fed by a DC/DC electronic power converter of the step-down type, a system that is known to have a nonlinear polynomial-type control input. [ABSTRACT FROM AUTHOR]

The two-dimensional (2D) Otsu algorithm used in image segmentation considers both the gray scale information of the image and the spatial information contained in the neighborhood of pixels. The algorithm is quite effective, but a number of variations have been proposed to improve its performance. In this paper, a new adaptive fractional-order (FO) genetic-particle swarm optimization (FOGPSO) version is proposed. The FOGPSO associates the particle selection operations of a genetic algorithm (GA) and particle swarm optimization (PSO). Crossover and genetic mutation are used to avoid PSO falling into a local optimum. Fractional calculus operators are adopted in the updating scheme of velocity and position, while the order of the derivative is adaptively changed according to the state of the particles. Compared with the original PSO, the integer PSO, the fractional PSO (FOPSO), other improved versions of the PSO for Otsu algorithms, and other existing methods for 2D Otsu algorithms, the proposed method shows great superiority. Indeed, experimental results reveal that both qualitatively and quantitatively, through suitable indices, as the regional contrast, the intersection over union (IOU) and peak signal to noise ratio (PSNR), the FOGPSO outperforms the other methods, thus verifying the effectiveness of the new algorithm. [ABSTRACT FROM AUTHOR]

This paper makes a new breakthrough in deliberating the bifurcations of fractional-order bidirectional associative memory neural network (FOBAMNN). In the beginning, the corresponding bifurcation results are established according to self-regulating parameter, which is different from bifurcation outcomes available by using time delay as the bifurcation parameter, and greatly enriches the bifurcation results of continuous neural networks(NNs). The deived results manifest that a larger self-regulating parameter is more conducive to the stability of the system, which is consistent with the actual meaning of the self-regulating parameter representing the decay rate of activity. In addition to the innovation in the research object, this paper also has innovation in the procedure of calculating the bifurcation critical point. In the face of the quartic equation about the bifurcation parameters, this paper utilizes the methodology of implicit array to calculate the bifurcation critical point succinctly and effectively, which eschews the disadvantages of the conventional Ferrari approach, such as cumbersome formula and huge computational efforts. Our developed technique can be employed as a general method to solve the bifurcation point including the problem of dealing with the bifurcation critical point of delay. Ultimately, numerical experiments test the key theoretical fruits of this paper. [ABSTRACT FROM AUTHOR]

This paper investigates the asymptotic stability and synchronization of fractional-order (FO) memristive neural networks with time delays. Based on the FO comparison principle and inverse Laplace transform method, the novel sufficient conditions for the asymptotic stability of a FO nonlinear system are given. Then, based on the above conclusions, the sufficient conditions for the asymptotic stability and synchronization of FO memristive neural networks with time delays are investigated. The results in this paper have a wider coverage of situations and are more practical than the previous related results. Finally, the validity of the results is checked by two examples. [ABSTRACT FROM AUTHOR]

Image deblurring is a fundamental image processing task, and research for efficient image deblurring methods is still a great challenge. Most of the currently existing methods are focused on TV-based models and regularization term construction; little efforts are paid to model proposal and correlated algorithms for the fidelity term in fractional-order derivative space. In this paper, we propose a novel fractional-order variational model for image deblurring, which can efficiently address three different blur kernels. The objective functional contains a fractional-order gradient fidelity term and a total generalized variation (TGV) regularization term, and it highlights the ability to preserve details and eliminate the staircase effect. To solve the problem efficiently, we provide two numerical algorithms based on the Chambolle-Pock primal-dual method (PD) and the alternating direction method of multipliers (ADMM). A series of experiments show that the proposed method achieves a good balance between detail preservation and deblurring compared with several existing advanced models. [ABSTRACT FROM AUTHOR]

Some comments are presented on the paper [N. Liu, J. Fang, W. Deng, Z.-J. Wu, and G.-Q. Dinng, International Journal of Control, Automation, and Systems, vo. 16, pp. 2839–2844, 2018]. Some counterexamples show that the main achievements in the above paper are incorrect. [ABSTRACT FROM AUTHOR]

This paper focuses on the quasi-stabilization of the quaternion-valued fractional-order memristive neural networks. Based on the contraction mapping theory, a sufficient condition is derived to ensure the existence of the equilibrium point for the memristive neural networks. Subsequently, by means of Lyapunov functional and fractional Laplace transform, a algebraic inequality-based condition is developed to guarantee the quasi-stability of the equilibrium point. In addition, a related question is whether the convex closure proposed by the quaternion parameters is meaningful, to overcome this issues, a vector ordering approach is proposed, which can be used to compare the "magnitude" of two different quaternions. Finally, the corresponding simulation results are included to show the effectiveness of the proposed methodology derived in this paper. [ABSTRACT FROM AUTHOR]

This paper studies the stability and bifurcation of n -dimensional fractional competitive website model with time delay. The system parameters are selected as bifurcation parameters, and the stability results and bifurcation criteria of the system are discussed. The theoretical results show that the stability region of the system can be extended or reduced by selecting appropriate system parameters. In addition, the effects of order and time delay on system dynamics are analyzed. The results show that the bifurcation can be delayed when the growth ability of website competition is small, the order is small or the competition between websites is large. Finally, numerical simulations verify the rationality of the theoretical results. [ABSTRACT FROM AUTHOR]

ABSTRACT Wireless power transfer (WPT) is an emerging technology that enables the wireless transfer of electrical energy from power supplies to electrical equipment. It has been widely used in electric vehicles, mobile phones, household appliances, medical devices, and other fields. However, the frequency splitting and bifurcation phenomena existing in WPT systems are the fundamental obstacles and challenges that affect the effective operation of WPT systems. In this paper, a method based on the fractional‐order circuit is proposed to simultaneously suppress the frequency splitting and bifurcation phenomena by changing the order of fractional‐order capacitor. By replacing the compensation capacitor in the transmitter of the traditional WPT system with a fractional‐order capacitor, a fractional‐order WPT system is formed. Then, using fractional calculus and circuit theory, the mathematical model of the proposed WPT system containing a fractional‐order capacitor is established, and the frequency splitting and bifurcation phenomena are analyzed. The theoretical results show that the frequency splitting and bifurcation phenomena are suppressed only by adjusting the order of fractional‐order capacitor, and the output power of the original resonant frequency is improved. Finally, the experimental prototype is implemented to validate the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, a novel non-convex fractional-order image denoising model is proposed to suppress the staircase effect produced by the TV model while maintaining a neat contour. The model combines ℓ q (0 < q < 1) quasi-norm and fractional-order regularization, and employs a diffusion coefficient with a faster convergence rate to preserve more image edges and details. Additionally, an adaptive regularization parameter is designed to adjust the denoising performance of the algorithm. To obtain the optimal approximate solution of the model, an enhanced primal-dual algorithm is adopted and the complexity and convergence of the algorithm are theoretically analyzed. Finally, the effectiveness of the proposed method is demonstrated through numerical experiments. • A new non-convex FOTV model is proposed. • A new diffusion coefficient is introduced to retain more edge details of the image. • The existing primal-dual algorithm is improved, and the convergence of this algorithm is analyzed. • An adaptive regularization parameter is designed. [ABSTRACT FROM AUTHOR]

This paper proposes a novel sliding mode control (SMC) algorithm for direct yaw moment control of four-wheel independent drive electric vehicles (FWID-EVs). The algorithm integrates adaptive law theory, fractional-order theory, and nonsingular terminal sliding mode reaching law theory to reduce chattering, handle uncertainty, and avoid singularities in the SMC system. A sequential quadratic programming (SQP) method is also proposed to optimize the yaw moment distribution under actuator constraints. The performance of the proposed algorithm is evaluated by a hardware-in-the-loop test with two driving maneuvers and compared with two existing SMC-based schemes together with the cases with the change of vehicle parameters and disturbances. The results demonstrate that the proposed algorithm can eliminate chattering and achieve the best lateral stability as compared with the existing schemes. [Display omitted] • A novel AFONT-SMC is proposed to achieve fast global convergence and precise tracking. • An adaptive law is proposed to avoid singularity and strengthen the system robustness. • A new boundary of full vehicle is studied to ensure the controllability of FWID-EVs. • Two new actuator constraints are studied to improve torque distribution in FWID-EVs. [ABSTRACT FROM AUTHOR]

The bifurcation phenomenon generated in neurons is considered to be the cause of many neurological diseases, thus, lots of investigators have been dedicated to bifurcation control, but most of them only focus on the integer-order neuronal models and control methods. Recently, increasing number of research works have shown that the differential equations of fractional-order are more appropriate for description of the electrical properties of certain nerve cell membranes. In this paper, we employ a fractional-order washout filter to realize bifurcation control for fractional-order Morris–Lecar neuronal model. Computer simulation verifies the effectiveness and improved performance of the proposed method than the integer-order washout filter. In addition, the analysis of the fractional-order controller's impacts on the model is also presented. [ABSTRACT FROM AUTHOR]