Master‐slave synchronization for coupled neural networks with Markovian switching topologies and stochastic perturbation

Abstract

Summary In this paper, the master‐slave synchronization for coupled neural networks with Markovian jumping topology and stochastic perturbation is discussed. Based on a graph theory, the ergodic property of the Markovian chain, and the strong law of the large numbers for local martingales, several sufficient conditions are established to ensure the almost sure exponential synchronization or asymptotic synchronization in mean square for coupled neural networks with Markovian jumping topology. By the pinning control method, the chaotic synchronization between the master system and the slave systems with stochastic disturbance is achieved. The effectiveness of the results is finally illustrated by a numerical example.

Chattering‐free adaptive sliding mode control for continuous‐time systems with time‐varying delay and process disturbance

“…s(t) guarantee that the trajectory of sliding mode s(t) will be attracted by the SMC law to the sliding surface and reaches it in finite time. In addition, one can intuitively see from Figure 3 that the curves of s 1 (t) and s 2 (t), respectively, reach the zero point during (48,49)T and (54,55)T, thus shows the effectiveness of Theorem 1. Under the variations of time-varying delay d(t) and process disturbance (t), the trajectories in Figure 4 show that the system states x(t) are reduced down and convergence to the equilibrium point gradually.…”

“…It can be found from (1) that the process disturbance (t) has a great influence to system state x(t). In most existing literatures, 17,[48][49][50] the intensity of the disturbance has a lower level than system state. Namely, the magnitude of each entry in D (t) is always less than that of system state Ax(t).…”

Exponential synchronization of chaotic systems with stochastic noise via periodically intermittent control

“…As is known to all, chaotic systems have high nonlinear dynamic characteristics and strong randomness, and it is difficult to achieve stability and synchronization by themselves. Until now, in many literatures, a series of control methods have been proposed to deal with various stability and synchronization problems, including the adaptive feedback control technique, the pinning control method, the master‐slave control technique, and the quantized control technique …”

Dissipativity of the stochastic Markovian switching CVNNs with randomly occurring uncertainties and general uncertain transition rates

“…Recently, some considerable results have been derived for the Markovian switching systems (Li, Liang, Gong, 2019;Luo et al, in press), where the neurons switch from one mode to another in a finite-modes set at different times. For example, almost sure asymptotic (or exponential) synchronisation has been addressed in Zhou et al (2018) for the coupled real-valued stochastic networks with switching topology. In Selvaraj et al (2018), finite-time synchronisation has been addressed for the stochastic coupled real-valued neural networks with input saturation and Markovian switching structure.…”