AbstrAct This chapter deals with the analysis problem of the global exponential stability for a general class of stochastic artificial higher order neural networks with multiple mixed time delays and Markovian jumping parameters. The mixed time delays under consideration comprise both the discrete time-varying delays and the distributed time-delays. The main purpose of this chapter is to establ...

In this paper, the global exponential stability analysis problem is considered for a class of recurrent neural networks (RNNs) with time delays and Markovian jumping parameters. The jumping parameters considered here are generated from a continuous-time discrete-state homogeneous Markov process, which are governed by a Markov process with discrete and finite state space. The purpose of the prob...

The Lévy, jumping process, defined in terms of the jumping size distribution and the waiting time distribution, is considered. The jumping rate depends on the process value. The fractional diffusion equation, which contains the variable diffusion coefficient, is solved in the diffusion limit. That solution resolves itself to the stretched Gaussian when the order parameter μ → 2. The truncation ...

We investigate the almost surely asymptotic stability of gene regulatory networks (GRNs) with Markovian switching. Previous research has described GRNs as coupled nonlinear stochastic systems under parametric perturbations without considering the important aspect of different time-delays in the subsystems. However, a realistic model of a GRN is that of a hybrid stochastic retarded system that r...

This paper studies the output tracking problem of continuous-time Markovian jumping systems (MJSs) via error feedback scheme. With the extension of output regulation to MJSs, sufficient conditions are obtained based on stochastic Lyapunov-Krasovskii functional. The resulting closed-loop system is guaranteed to be stochastically stable and the output tracking is achieved almost asymptotically. M...