Adaptive Exponential Synchronization of Multislave Time-Delayed Recurrent Neural Networks With Lévy Noise and Regime Switching.

This paper discusses the problem of adaptive exponential synchronization in mean square for a new neural network model with the following features: 1) the noise is characterized by the Lévy process and the parameters of the model change in line with the Markovian process; 2) the master system is also disturbed by the same Lévy noise; and 3) there are multiple slave systems, and the state matrix of each slave system is an affine function of the state matrices of all slave systems. Based on the Lyapunov functional theory, the generalized Itô's formula, -matrix method, and the adaptive control technique, some criteria are established to ensure the adaptive exponential synchronization in the mean square of the master system and each slave system. Moreover, the update law of the control gain and the dynamic variation of the parameters of the slave systems are provided.

Adaptive synchronization for neutral-type neural networks with stochastic perturbation and Markovian switching parameters.

In this paper, the problem of adaptive synchronization is investigated for stochastic neural networks of neutral-type with Markovian switching parameters. Using the M-matrix approach and the stochastic analysis method, some sufficient conditions are obtained to ensure three kinds of adaptive synchronization for the stochastic neutral-type neural networks. These three kinds of adaptive synchronization include the almost sure asymptotical synchronization, exponential synchronization in p th moment and almost sure exponential synchronization.