Exponential Stability for Impulsive BAM Neural Networks with Time-Varying Delays and Reaction-Diffusion Terms

Abstract

Impulsive bidirectional associative memory neural network model with time-varying delays and reaction-diffusion terms is considered. Several sufficient conditions ensuring the existence, uniqueness, and global exponential stability of equilibrium point for the addressed neural network are derived by M-matrix theory, analytic methods, and inequality techniques. Moreover, the exponential convergence rate index is estimated, which depends on the system parameters. The obtained results in this paper are less restrictive than previously known criteria. Two examples are given to show the effectiveness of the obtained results.

Dynamic Analysis of Stochastic Reaction-Diffusion Cohen-Grossberg Neural Networks with Delays

“…The delayed neural networks with diffusion terms can commonly be expressed by partial functional differential equation PFDE . To study the stability of delayed reaction-diffusion neural networks, for instance, see [24][25][26][27][28][29][30][31] , and references therein.…”

Mean square exponential stability of stochastic genetic regulatory networks with time-varying delays

“…To the best of our knowledge, the exponential stability for GRN with time-varying delays is rarely considered although some researchers have studied the exponential stability of delayed neural networks [6,30,36]. We found only one relevant paper [4] about this topic.…”

“…However, the genetic regulatory network under study was a deterministic model without stochastic perturbations. Recently, the stability of neural networks with stochastic perturbations or parameter uncertainties were studied [6,16,17,[21][22][23][24][25]30,35,36,39]. They provided some clues in analyzing genetic regulatory networks.…”

Mean-square exponential stability of fuzzy stochastic BAM networks with hybrid delays

“…Song and Zhao [12] provided a stability criterion of complex-valued neural networks with both leakage delay and time-varying delays on time scales. Song and Cao [13] proved the exponential stability for a class of impulsive BAM neural networks with time-varying delays and reaction-diffusion terms. See and the references therein for more information on the study of stability problems for deterministic BAMNs.…”