Global Mittag-Leffler stability and synchronization of memristor-based fractional-order neural networks

The present paper introduces memristor-based fractional-order neural networks. The conditions on the global Mittag-Leffler stability and synchronization are established by using Lyapunov method for these networks. The analysis in the paper employs results from the theory of fractional-order differential equations with discontinuous right-hand sides. The obtained results extend and improve some previous works on conventional memristor-based recurrent neural networks.     

Stability and synchronization of memristor-based fractional-order delayed neural networks

Global asymptotic stability and synchronization of a class of fractional-order memristor-based delayed neural networks are investigated. For such problems in integer-order systems, Lyapunov–Krasovskii functional is usually constructed, whereas similar method has not been well developed for fractional-order nonlinear delayed systems. By employing a comparison theorem for a class of fractional-order linear systems with time delay, sufficient condition for global asymptotic stability of fractional memristor-based delayed neural networks is derived. Then, based on linear error feedback control, the synchronization criterion for such neural networks is also presented. Numerical simulations are given to demonstrate the effectiveness of the theoretical results.     

Global almost sure self-synchronization of Hopfield neural networks with randomly switching connections

In this paper, we discuss Hopfield neural networks with stochastic switching weights, investigating their global almost sure self-synchronization. Sufficient conditions ensuring global almost sure exponential synchronization of Hopfield neural networks with stochastic switching weights are given.     

Global exponential periodicity and global exponential stability of a class of recurrent neural networks with various activation functions and time-varying delays

The paper presents theoretical results on the global exponential periodicity and global exponential stability of a class of recurrent neural networks with various general activation functions and time-varying delays. The general activation functions include monotone nondecreasing functions, globally Lipschitz continuous and monotone nondecreasing functions, semi-Lipschitz continuous mixed monotone functions, and Lipschitz continuous functions. For each class of activation functions, testable algebraic criteria for ascertaining global exponential periodicity and global exponential stability of a class of recurrent neural networks are derived by using the comparison principle and the theory of monotone operator. Furthermore, the rate of exponential convergence and bounds of attractive domain of periodic oscillations or equilibrium points are also estimated. The convergence analysis based on the generalization of activation functions widens the application scope for the model design of neural networks. In addition, the new effective analytical method enriches the toolbox for the qualitative analysis of neural networks.     

Global exponential synchronization of memristor-based recurrent neural networks with time-varying delays

This paper deals with the problem of global exponential synchronization of a class of memristor-based recurrent neural networks with time-varying delays based on the fuzzy theory and Lyapunov method. First, a memristor-based recurrent neural network is designed. Then, considering the state-dependent properties of the memristor, a new fuzzy model employing parallel distributed compensation (PDC) gives a new way to analyze the complicated memristor-based neural networks with only two subsystems. Comparisons between results in this paper and in the previous ones have been made. They show that the results in this paper improve and generalized the results derived in the previous literature. An example is also given to illustrate the effectiveness of the results.     

Global exponential periodicity and stability of discrete-time complex-valued recurrent neural networks with time-delays

In recent years, complex-valued recurrent neural networks have been developed and analysed in-depth in view of that they have good modelling performance for some applications involving complex-valued elements. In implementing continuous-time dynamical systems for simulation or computational purposes, it is quite necessary to utilize a discrete-time model which is an analogue of the continuous-time system. In this paper, we analyse a discrete-time complex-valued recurrent neural network model and obtain the sufficient conditions on its global exponential periodicity and exponential stability. Simulation results of several numerical examples are delineated to illustrate the theoretical results and an application on associative memory is also given.     

Global exponential stability of impulsive high-order BAM neural networks with time-varying delays

In this paper, global exponential stability and exponential convergence are studied for a class of impulsive high-order bidirectional associative memory (BAM) neural networks with time-varying delays. By employing linear matrix inequalities (LMIs) and differential inequalities with delays and impulses, several sufficient conditions are obtained for ensuring the system to be globally exponentially stable. Three illustrative examples are also given at the end of this paper to show the effectiveness of our results.     

New conditions for global exponential stability of cellular neural networks with delays

In this paper, we study further a class of cellular neural networks model with delays. By employing the inequality , constructing a new Lyapunov functional, and applying the Homeomorphism theory, we derive some new conditions ensuring the existence, uniqueness of the equilibrium point and its global exponential stability for cellular neural networks. These conditions are independent of delays and posses infinitely adjustable real parameters, which are of highly important significance in the designs and applications of networks. In addition, we extend or improve the previously known results.     

Criteria for exponential stability of Cohen–Grossberg neural networks

In this paper, the Cohen–Grossberg neural network models without and with time delays are considered. By constructing several novel Lyapunov functionals, some sufficient criteria for the existence of a unique equilibrium and global exponential stability of the network are derived. These results are fairly general and can be easily verified. Besides, the approach of the analysis allows one to consider different types of activation functions, including piecewise linear, sigmoids with bounded activations as well as C¹-smooth sigmoids. In the meantime, our approach does not require any symmetric assumption of the connection matrix. It is believed that these results are significant and useful for the design and applications of the Cohen–Grossberg model.     

Existence and global exponential stability of a periodic solution to interval general bidirectional associative memory (BAM) neural networks with multiple delays on time scales

In this paper, we first investigate the existence of a periodic solution to interval general bidirectional associative memory (BAM) neural networks with multiple delays on time scales by the continuation theorem of coincidence degree theory. Then, by constructing a Lyapunov functional, we discuss the global exponential stability of the periodic solution for such neural networks on time scales. The paper unifies periodic discrete-time and continuous-time BAM neural networks under the same framework.     

Further results on robustness analysis of global exponential stability of recurrent neural networks with time delays and random disturbances

In this paper, further results on robustness analysis of global exponential stability of recurrent neural networks (RNNs) subjected to time delays and random disturbances are provided. Novel exponential stability criteria for the RNNs are derived, and upper bounds of the time delay and noise intensity are characterized by solving transcendental equations containing adjustable parameters. Through the selection of the adjustable parameters, the upper bounds are improved. It shows that our results generalize and improve the corresponding results of recent works. In addition, some numerical examples are given to show the effectiveness of the results we obtained.     

Novel conditions on exponential stability of a class of delayed neural networks with state-dependent switching

This paper is concerned with the global exponential stability on a class of delayed neural networks with state-dependent switching. Under the novel conditions, some sufficient criteria ensuring exponential stability of the proposed system are obtained. In particular, the obtained conditions complement and improve earlier publications on conventional neural networks with continuous or discontinuous right-hand side. Numerical simulations are also presented to illustrate the effectiveness of the obtained results.     

Global exponential stability of interval general BAM neural networks with reaction-diffusion terms and multiple time-varying delays

In this paper, we first discuss the existence and uniqueness of the equilibrium point of interval general BAM neural networks with reaction-diffusion terms and multiple time-varying delays by means of using degree theory. Then by applying the existence result of an equilibrium point and constructing a Lyapunov functional, we discuss global exponential stability for above neural networks. In the last section, we also give an example to demonstrate the validity of our global exponential stability result for above neural network.     

New synchronization criteria for memristor-based networks: Adaptive control and feedback control schemes

In this paper, we investigate synchronization for memristor-based neural networks with time-varying delay via an adaptive and feedback controller. Under the framework of Filippov’s solution and differential inclusion theory, and by using the adaptive control technique and structuring a novel Lyapunov functional, an adaptive updated law was designed, and two synchronization criteria were derived for memristor-based neural networks with time-varying delay. By removing some of the basic literature assumptions, the derived synchronization criteria were found to be more general than those in existing literature. Finally, two simulation examples are provided to illustrate the effectiveness of the theoretical results.