Mean-square stabilization of impulsive neural networks with mixed delays by non-fragile feedback involving random uncertainties.

In this paper, we consider a class of neural networks with mixed delays and impulsive interferences. Firstly, a sufficient condition is given to ensure the existence and uniqueness of the equilibrium point of the proposed neural networks by employing the contraction mapping theorem. Secondly, we discuss the issue of the exponential stability in mean-square of the equilibrium point by a non-fragilely delayed output coupling feedback which involves stochastically occurring gain oscillations.

Synchronization of Uncertain Coupled Neural Networks With Time-Varying Delay of Unknown Bound via Distributed Delayed Impulsive Control.

This article investigates the issue of synchronization for a type of uncertain coupled neural networks (CNNs) involving time-varying delay with unmeasured or unknown bound by delayed impulsive control with distributed delay. A new Halanay-like delayed differential inequality is presented, and both cases of impulsive control and impulsive perturbation are well-considered. Stemmed from this new inequality and techniques of linear matrix inequalities (LMIs), some sufficient criteria are obtained to achieve both dynamically and statically global μ -synchronization of the delayed CNNs, and a distributed-delay-dependent impulsive controller is designed.

Dynamic behaviors of the FitzHugh-Nagumo neuron model with state-dependent impulsive effects.

In present work, in order to reproduce spiking and bursting behavior of real neurons, a new hybrid biological neuron model is established and analyzed by combining the FitzHugh-Nagumo (FHN) neuron model, the threshold for spike initiation and the state-dependent impulsive effects (impulse resetting process). Firstly, we construct Poincaré mappings under different conditions by means of geometric analysis, and then obtain some sufficient criteria for the existence and stability of order-1 or order-2 periodic solution to the impulsive neuron model by finding the fixed point of Poincaré mapping and some geometric analysis techniques. Numerical simulations are given to illustrate and verify our theoretical results.