ABSTRACT
In the brief, delayed impulsive control is investigated for the synchronization of chaotic neural networks. In order to overcome the difficulty that the delays in impulsive control input can be flexible, we utilize the concept of average impulsive delay (AID). To be specific, we relax the restriction on the upper/lower bound of such delays, which is not well addressed in most existing results. Then, by using the methods of average impulsive interval (AII) and AID, we establish a Lyapunov-based relaxed condition for the synchronization of chaotic neural networks. It is shown that the time delay in impulsive control input may bring a synchronizing effect to the chaos synchronization. Furthermore, we use the method of linear matrix inequality (LMI) for designing average-delay impulsive control, in which the delays satisfy the AID condition. Finally, an illustrative example is given to show the validity of the derived results.
Subject(s)
Algorithms , Neural Networks, Computer , Time FactorsABSTRACT
In the paper, synchronization of coupled neural networks with delayed impulses is investigated. In order to overcome the difficulty that time delays can be flexible and even larger than impulsive interval, we propose a new method of average impulsive delay (AID). By the methods of average impulsive interval (AII) and AID, some sufficient synchronization criteria for coupled neural networks with delayed impulses are obtained. We prove that the time delay in impulses can play double roles, namely, it may desynchronize a synchronous network or synchronize a nonsynchronized network. Moreover, a unified relationship is established among AII, AID and rate coefficients of the impulsive dynamical network such that the network is globally exponentially synchronized (GES). Further, we discuss the case that time delays in impulses may be unbounded, which has not been considered in existing results. Finally, two examples are presented to demonstrate the validity of the derived results.
