Synchronization of nonidentical chaotic neural networks with leakage delay and mixed time-varying delays

Abstract

In this paper, an integral sliding mode control approach is presented to investigate synchronization of nonidentical chaotic neural networks with discrete and distributed time-varying delays as well as leakage delay. By considering a proper sliding surface and constructing Lyapunov-Krasovskii functional, as well as employing a combination of the free-weighting matrix method, Newton-Leibniz formulation and inequality technique, a sliding mode controller is designed to achieve the asymptotical synchronization of the addressed nonidentical neural networks. Moreover, a sliding mode control law is also synthesized to guarantee the reachability of the specified sliding surface. The provided conditions are expressed in terms of linear matrix inequalities, and are dependent on the discrete and distributed time delays as well as leakage delay. A simulation example is given to verify the theoretical results.

Synchronization of a Class of Switched Neural Networks with Time-Varying Delays via Nonlinear Feedback Control

“…Then the conditions of Corollary 1 are satisfied. It follows from Corollary 1 that system (34) and the corresponding response system (35) are exponentially synchronized with the nonlinear controller (36). Choose 100 random initial conditions, Fig.…”

“…Choose 100 random initial conditions, the synchronization errors e 1 (t) and e 2 (t) between the drive system (34) and the corresponding response system(35) with the nonlinear controller(36).…”

Robust decentralized adaptive synchronization of general complex networks with coupling delayed and uncertainties

“…Therefore, the understanding of synchronization for complex networks is still insufficient. On the one hand, there are some restrictions in coupling matrices such as symmetric or irreducible [65][66][67][68][69][70][71][72][73][74][75][76]. On the other hand, it is also assumed that the derivative of the time-varying coupling delay is less than one [14,17,23,24,40,43], or only considering the constant time-delay [2,5,18,23,25,30], which are the second and third key problems discussed here.…”

Sliding-mode synchronization for nonidentical Markovian jump neural networks with leakage delay and partially unknown transition probabilities

“…In the literature, however, synchronization in chaotic neural networks mainly focus on the synchronization of two chaotic identical neural networks by using various control methods such as adaptive control [6], impulsive control [7], sampleddata control [8], linear feedback control ( including static feedback control [9] and dynamic feedback control [10]), timedelay feedback control [11], periodically intermittent control [12], etc.. By contrast, synchronization of two non-identical chaotic systems has not been widely studied [13]- [15]. However, it is of great significance to study the synchronization problem of nonidentical chaotic systems because of its practical applications, for example, the adaptive synchronization of two different chaotic systems has been used to develop an asymmetric image cryptosystem [16].…”