Different impulsive effects on synchronization of fractional-order memristive BAM neural networks

This paper considered exponential synchronization in fractional-order memristive BAM neural networks (FMBAMNNs) with time delay via switching jumps mismatch. Exponential function is introduced for studying fractional-order differential system. According to double-layer structure of FMBAMNNs, two controllers are designed for the response FMBAMNNs. Particularly, more wide ranges of impulsive effects, which are affected by fractional-order \(\alpha \), are discussed in detail. One case is that the impulsive effect contributes to system convergence, and the other is that the impulsive effect destroys the system convergence. Based on the fractional stability theory and the definition of average impulsive interval, several criteria for achieving synchronization of FMBAMNNs are established. For different impulsive effects, the rate of convergence is precisely expressed. Finally, numerical examples verify the validity of the theoretical results.     

GLOBAL DYNAMICS OF DELAYED BIDIRECTIONAL ASSOCIATIVE MEMORY （BAM） NEURAL NETWORKS

IntroductionConsiderthebidirectionalassociativememory (BAM )neuralnetworkswithconstanttransmissiondelaysdescribedbyasystemofdelaydifferentialequationsoftheform[1,2 ]:dxi(t)dt =-aixi(t) nj=1bijfj(yj(t-σij) ) Ii,　　i=1 ,2 ,… ,m ,dyj(t)dt =-cjyj(t) mi=1djigi(xi(t-τji) ) Jj,　　j=1 ,2 ,… ,n ,fort >0 .Thesystem ( 1 )consistsoftwosetsofneurons (orunits)arrangedontwolayers,namely ,I_layerandJ_layer.Inthesystem ( 1 ) ,xi( ·)andyj( ·)denotemembranepotentialoftheithneuronsfromtheI_laye…     

Periodically intermittent control strategies for $$\varvec{\alpha }$$-exponential stabilization of fractional-order complex-valued delayed neural networks

This paper studies the global \(\alpha \)-exponential stabilization of a kind of fractional-order neural networks with time delay in complex-valued domain. To end this, several useful fractional-order differential inequalities are set up, which generalize and improve the existing results. Then, a suitable periodically intermittent control scheme with time delay is put forward for the global \(\alpha \)-exponential stabilization of the addressed networks, which include feedback control as a special case. Utilizing these useful fractional-order differential inequalities and combining with the Lyapunov approach and other inequality techniques, some novel delay-independent criteria in terms of real-valued algebraic inequalities are obtained to ensure global \(\alpha \)-exponential stabilization of the discussed networks, which are very simple to implement in practice and avert to calculate the complex matrix inequalities. Finally, the availability of the theoretical criteria is verified by an illustrative example with simulations.     

Sampled-data-based lag synchronization of chaotic delayed neural networks with impulsive control

Nonlinear Dynamics - In the framework of sampled-data control, this paper deals with the lag synchronization of chaotic neural networks with time delay meanwhile taking the impulsive control into...     

Cluster synchronization of coupled delayed competitive neural networks with two time scales

Nonlinear Dynamics - This paper investigates the cluster synchronization problem of coupled delayed competitive neural networks (CNNs) with two time scales. Each CNN contains short- and long-term...     

Exponential synchronization of chaotic neural networks: a matrix measure approach

Based on matrix measure and Halanay inequality, exponential synchronization of a class of chaotic neural networks with time-varying delays is investigated. Without constructing Lyapunov function, some simple but generic criteria for exponential synchronization of chaotic neural networks are derived. It is shown that the obtained results are easy to verify and simple to implement in practice. Two examples are given to illustrate the effectiveness of the presented synchronization scheme.     

Global synchronization of stochastic delayed complex networks

This paper is concerned with the delay-dependent synchronization criterion for stochastic complex networks with time delays. Firstly, expectations of stochastic cross terms containing the It? integral are investigated by utilizing stochastic analysis techniques. In fact, in order to obtain less conservative delay-dependent conditions for stochastic delay systems including stochastic complex (or neural) networks with time delays, how to deal with expectations of these stochastic cross terms is an important problem, and expectations of these stochastic terms were not dealt with properly in many existing results. Then, based on the investigation of expectations of stochastic cross terms, this paper proposes a novel delay-dependent synchronization criterion for stochastic delayed complex networks. In the derivation process, the mathematical development avoids bounding stochastic cross terms. Thus, the method leads to a simple criterion and shows less conservatism. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed approach.     

Exponential synchronization of stochastic delayed discrete-time complex networks

This paper is concerned with the problem of synchronization for stochastic discrete-time drive-response networks with time-varying delay. By employing the Lyapunov functional method combined with the stochastic analysis as well as the feedback control technique, several sufficient conditions are established that guarantee the exponentially mean-square synchronization of two identical delayed networks with stochastic disturbances. These sufficient conditions, which are expressed in terms of linear matrix inequalities (LMIs), can be solved efficiently by the LMI toolbox in Matlab. A particular feature of the LMI-based synchronization criteria is that they are dependent not only on the connection matrices in the drive networks and the feedback gains in the response networks, but also on the lower and upper bounds of the time-varying delay, and are therefore less conservative than the delay-independent ones. Two numerical examples are exploited to demonstrate the feasibility and applicability of the proposed synchronization approaches.     

Delay-independent stability criteria for complex-valued BAM neutral-type neural networks with time delays

This paper focuses on the global asymptotic stability of complex-valued bidirectional associative memory (BAM) neutral-type neural networks with time delays. By virtue of homeomorphism theory, inequality techniques and Lyapunov functional, a set of delay-independent sufficient conditions is established for assuring the existence, uniqueness and global asymptotic stability of an equilibrium point of the considered complex-valued BAM neutral-type neural network model. The assumption on boundedness of the activation functions is not required, and the LMI-based criteria are easy to be checked and executed in practice. Finally, we give one example with simulation to show the applicability and effectiveness of our main results.     

Adaptive synchronization of uncertain dynamical networks with delayed coupling

We propose a simple scheme for the synchronization of an uncertain complex dynamical network with delayed coupling. Based on the Lyapunov stability theory of functional differential equations, certain controllers can be designed for ensuring the states of uncertain dynamical network with coupling delays to globally asymptotically synchronize by combining the adaptive method and linear feedback with the updated feedback strength. Different update gains η _i will lead to different rates toward synchrony, the choice of which depends on the concrete systems and network models. This strategy can be applied to any complex dynamical network (regular, small-world, scale-free or random). Numerical examples with respectively nearest-neighbor coupling and scale-free structure are given to demonstrate the effectiveness of our presented scheme.     

Robust synchronization of uncertain chaotic neural networks with randomly occurring uncertainties and non-fragile output coupling delayed feedback controllers

This paper deals with the synchronization control problem for the uncertain chaotic neural networks with randomly occurring uncertainties and randomly occurring control gain fluctuations. By introducing an improved Lyapunov–Krasovskii functional and employing reciprocally convex approach, a delay-dependent non-fragile output feedback controller is designed to achieve synchronization with the help of a drive–response system and the linear matrix inequality approach. Finally, numerical results and its simulations are given to show the effectiveness of the derived results.     

State estimation for switched discrete-time stochastic BAM neural networks with time varying delay

This paper focuses the issue of state estimation for a class of switched discrete-time stochastic bidirectional associative memory (BAM) neural networks with time varying delay. The main purpose of this paper is to estimate the neuron states through available output measurements such that the dynamics of the error state system to be robustly exponentially stable. By employing average dwell time approach together with piecewise Lyapunov functional technique, a set of sufficient conditions is derived with respect to all admissible uncertainties, to guarantee the existence of the desired state estimator for the uncertain switched discrete-time BAM delayed neural networks. Specifically, we derive sufficient conditions to achieve robust state estimation with the characterization of complex effects of time delays, parameter uncertainties, and stochastic perturbations. In particular, the parameter uncertainties are assumed to be time varying and unknown, but norm bounded. It should be mentioned that our estimation results are delay dependent, which depend on not only the upper bounds of time delay, but also their lower bounds. More precisely, the desired estimator matrix gain is obtained in terms of the solution of the derived LMIs. Finally, numerical examples with a simulation result are given to illustrate the effectiveness and applicability of the obtained results.     

New sufficient conditions on global asymptotic synchronization of inertial delayed neural networks by using integrating inequality techniques

Nonlinear Dynamics - In this paper, the global asymptotic synchronization of a class of inertial delayed neural networks is investigated. Instead of using conventional study methods of global...     

Noise-to-state practical stability and stabilization of random neural networks

Nonlinear Dynamics - This paper is devoted to studying noise-to-state practical stability and stabilization problems for random neural networks in the presence of general disturbances. It is proved...     

Synchronization of chaotic-type delayed neural networks and its application

Nonlinear Dynamics - In this paper, the authors analyze a time-fractional advection–diffusion equation, involving the Riemann–Liouville derivative, with a nonlinear source term. They...     

Exponential state estimation for delayed recurrent neural networks with sampled-data

In this paper, the sampled-data state estimation problem is investigated for a class of recurrent neural networks with time-varying delay. Instead of the continuous measurement, the sampled measurement is used to estimate the neuron states, and a sampled-data estimator is constructed. By converting the sampling period into a bounded time-varying delay, the error dynamics of the considered neural network is derived in terms of a dynamic system with two different time-delays. Subsequently, by choosing an appropriate Lyapunov functional and using the Jensen??s inequality, a sufficient condition depending on the sampling period is obtained under which the resulting error system is exponentially stable. Then a sampled-data estimator is designed in terms of the solution to a set of linear matrix inequalities (LMIs) which can be solved by using available software. Finally, a numerical example is employed to demonstrate the effectiveness of the proposed sampled-data estimation approach.     

Synchronization error bound of chaotic delayed neural networks

Synchronization of master–slave chaotic neural networks are well studied through asymptotic and exponential stability of error dynamics. Besides qualitative properties of error dynamics, there is a need to quantify the error in real-time experiments especially in secure communication system. In this article, we focused on quantitative analysis of error dynamics by finding the exact analytical error bound for the synchronization of delayed neural networks. Using the Halanay inequality, the error bound is going to be obtained in terms of exponential of given system parameters and delay. The time-varying coupling delay has been considered in the neural networks which does not require any restrictive condition on the derivative of the delay. The proposed method can also be applied to find error bound for state estimation problem. The analytical synchronization bound has been corroborated by two examples.     

Delay-dependent state estimation for T-S fuzzy delayed Hopfield neural networks

This paper proposes a new delay-dependent state estimator for Takagi–Sugeno (T-S) fuzzy delayed Hopfield neural networks. By employing a suitable Lyapunov–Krasovskii functional, a delay-dependent criterion is established to estimate the neuron states through available output measurements such that the dynamics of the estimation error is asymptotically stable. It is shown that the design of the proposed state estimator for such neural networks can be achieved by solving a linear matrix inequality (LMI), which can be easily facilitated by using some standard numerical packages. An illustrative example is given to demonstrate the effectiveness of the proposed state estimator.