Existence and exponential stability of periodic solution for stochastic Hopfield neural networks on time scales

Hybrid impulsive and switching Hopfield neural networks with state-dependent impulses

We discuss the global stability of switching Hopfield neural networks (HNN) with state-dependent impulses using B-equivalence method. Under certain conditions, we show that the state-dependent impulsive switching systems can be reduced to the fixed-time ones, and that the global stability of corresponding comparison system implies the same stability of the considered system. On this basis, a novel stability criterion for the considered HNN is established. Finally, two numerical examples are given to demonstrate the effectiveness of our results.

Passivity analysis of uncertain stochastic neural networks with time-varying delays and Markovian jumping parameters

This paper investigates the problem of robust passivity of uncertain stochastic neural networks with time-varying delays and Markovian jumping parameters. To reflect most of the dynamical behaviors of the system, both parameter uncertainties and stochastic disturbances are considered; stochastic disturbances are given in the form of a Brownian motion. By utilizing the Lyapunov functional method, the Itô differential rule, and matrix analysis techniques, we establish a sufficient criterion such that, for all admissible parameter uncertainties and stochastic disturbances, the stochastic neural network is robustly passive in the sense of expectation. A delay-dependent stability condition is formulated, in which the restriction of the derivative of the time-varying delay should be less than 1 is removed. The derived criteria are expressed in terms of linear matrix inequalities that can be easily checked by using the standard numerical software. Illustrative examples are presented to demonstrate the effectiveness and usefulness of the proposed results.