Global Stability and Synchronization of Markovian Switching Neural Networks with Stochastic Perturbation and Impulsive Delay

Abstract

This paper focuses on the hybrid effects of Markovian switching, stochastic perturbation, and impulsive delay on neural networks. First, some novel generic criteria for Markovian switching neural networks with stochastic perturbation and impulsive delay are derived by establishing an extended Halanay differential inequality on impulsive dynamical systems. Second, our sufficient conditions ensuring synchronization are dependent on coupling and impulsive delay, and show coupling and impulsive effects on the synchronization of neural networks. Finally, simulation results demonstrate the effectiveness of the theoretical results.

A Novel Method of Realizing Stochastic Chaotic Secure Communication by Synchrosqueezed Wavelet Transform: The Finite-Time Case

“…Remark 2: Theorem 1 provides an effective method to design the desired controller by (9). In fact, given scalars 1 , , η θ ρ and 2 ρ , one can obtain the desired feedback gains i k by solving (10). Remark 3: In secure communication, we can estimate the synchronization time 1 t by ( 13), to ensure the decryption after the systems achieved the complete synchronization.…”

“…In addition, stochastic effects exist in real systems. A lot of dynamical systems have variable structures subject to stochastic abrupt changes, which may result in abrupt phenomena such as stochastic failures and repairs of components, changes in the interconnections of subsystems, sudden environment changes [10][11], etc. Therefore, it is necessary to study the stability of stochastic chaotic system in finite-time for secure communication.…”