Yi Shen

Global exponential periodicity and stability of a class of memristor-based recurrent neural networks with multiple delays

The paper presents theoretical results on the global exponential periodicity and stability of a class of memristor-based recurrent neural networks with multiple delays. The dynamic analysis in the paper employs the theory of differential equations with discontinuous right-hand side as introduced by Filippov. By using the inequality techniques and a useful Lyapunov functional, some new testable algebraic criteria are obtained for ensuring the existence and global exponential stability of periodic solution of the system. The model based on the memristor widens the application scope for the design of neural networks, and the new effective results also enrich the toolbox for the qualitative analysis of neural networks.

Compound synchronization of four memristor chaotic oscillator systems and secure communication

In this paper, a novel kind of compound synchronization among four chaotic systems is investigated, where the drive systems have been conceptually divided into two categories: scaling drive systems and base drive systems. Firstly, a sufficient condition is obtained to ensure compound synchronization among four memristor chaotic oscillator systems based on the adaptive technique. Secondly, a secure communication scheme via adaptive compound synchronization of four memristor chaotic oscillator systems is presented. The corresponding theoretical proofs and numerical simulations are given to demonstrate the validity and feasibility of the proposed control technique. The unpredictability of scaling drive systems can additionally enhance the security of communication. The transmitted signals can be split into several parts loaded in the drive systems to improve the reliability of communication.

Global exponential stability of a class of memristor-based recurrent neural networks with time-varying delays

The paper analyzes a general memristor-based recurrent neural networks with time-varying delays (DRNNs). The dynamic analysis in the paper employs results from the theory of differential equations with discontinuous right-hand side as introduced by Filippov, and some new conditions concerning global exponential stability are obtained. In addition, these conditions do not require the activation functions to be differentiable, the connection weight matrices to be symmetric and the delay functions to be differentiable, our results are mild and more general. Finally, numerical simulations illustrate the effectiveness of our results.

Compound synchronization for four chaotic systems of integer order and fractional order

By combining the tracking control and the stability theory of nonlinear fractional-order systems, a novel kind of compound synchronization among four chaotic systems of integer order and fractional order has been investigated, where the drive systems have been conceptually divided into two categories: the scaling drive system and the base drive system. A fractional-order chaotic system can realize compound synchronization with the novel system, which is a combination system among two integer-order chaotic systems and one different fractional-order chaotic system. Numerical simulation results are presented to demonstrate the effectiveness and correctness of the compound synchronization.

Passivity analysis of stochastic delayed neural networks with Markovian switching

In this paper, the problem of passivity analysis is investigated for a class of stochastic delayed neural networks with Markovian switching. By applying Lyapunov functional and free-weighting matrix, delay-dependent/independent passivity criteria are presented in terms of linear matrix inequalities. The results herein include existing ones for neural networks without Markovian switching as special cases. An example is given to demonstrate the effectiveness of the proposed criteria.

H∞ Synchronization of Directed Complex Dynamical Networks with Mixed Time-Delays and Switching Structures

This paper is concerned with the H∞ synchronization problem of directed complex dynamical networks. For the system under study, mixed time-delays and stochastic factors are taken into consideration. By stochastic analysis techniques, we establish sufficient conditions under which the network is synchronized to the prescribed system in the H∞ sense. Moreover, the effect of exogenous disturbance on synchronization performance is reduced to a given H∞ norm. Finally, numerical simulations are given to verify the usefulness and effectiveness of our results.

New results on passivity analysis of memristor-based neural networks with time-varying delays

In this paper, the passivity problem of memristor-based neural networks (MNNs) with time-varying delays is investigated. New delay-dependent criteria are established for the passivity of MNNs. The time-varying delays of our paper are not necessary to be differentiable, so our results are less conservative, which enrich and improve the earlier publications. An example is given to demonstrate the effectiveness of the obtained results.

Stability of non-autonomous bidirectional associative memory neural networks with delay

The paper discusses the stability of non-autonomous bidirectional associative memory neural networks. The existence and uniqueness of periodic solutions of the neural networks are investigated by using Gaines and Mawhins continuation theorem of coincidence degree theory in the paper. Moreover, criterions on asymptotic stability and exponential stability of periodic solutions of the neural networks are obtained by using matrix function inequality, and algorithms for the criterions on the neural networks are provided. Some of the results in the paper generalize and improve the results in the existing references. In the end, an illustrate example is given to verify our results.

Exponential synchronization of coupled fuzzy neural networks with disturbances and mixed time-delays

This paper focuses on the exponential synchronization problem of coupled fuzzy neural networks with disturbances and mixed time-delays. For the network under study, the effects of both random and vague factors are considered. By stochastic analysis techniques, we establish sufficient conditions for the coupled fuzzy neural networks to be exponentially synchronized in the mean square. It is demonstrated that the network synchronizability is largely dependent on the coupling structure of such network. Moreover, the information exchange network needs not to be undirected or strongly connected. Finally, numerical simulations are given to verify the usefulness and effectiveness of our results.

Improved reachable set bounding for linear time-delay systems with disturbances

Abstract In this paper, we reconsider the problem of reachable set bounding for linear time-delay systems with disturbances. Generalized reachable sets for dynamical systems are proposed where initial points are taken into account. Meanwhile, a novel lemma is given which shows an extended criterion that the reachable sets are bounded. Then, based on this lemma and the Lyapunov–Krasovskii functional (LKF) as well as the free-weighting matrix techniques, improved delay-dependent linear matrix inequality (LMI) criteria are obtained for finding an ellipsoid to bound the reachable sets of linear time-delay systems with disturbances. Two numerical examples are finally provided to substantiate the efficiency and merits of our theoretical results.