Abstract
We discuss the dynamical behaviors of impulsive stochastic reaction-diffusion neural networks (ISRDNNs) with mixed time delays. By using a well-knownL-operator differential inequality with mixed time delays and combining with the Lyapunov-Krasovkii functional approach, as well as linear matrix inequality (LMI) technique, some novel sufficient conditions are derived to ensure the existence, uniqueness, and global exponential stability of the periodic solutions for ISRDNNs with mixed time delays in the mean square sense. The obtained sufficient conditions depend on the reaction-diffusion terms. The results of this paper are new and improve some of the previously known results. The proposed model is quite general since many factors such as noise perturbations, impulsive phenomena, and mixed time delays are considered. Finally, two numerical examples are provided to verify the usefulness of the obtained results.
Highlights
In recent years, neural networks NNs with time delays have received considerable attention due to their extensive applications in solving some optimization problems, associative memory, classification of patterns, and other areas
We investigate dynamical behaviors of ISRDNNs with Dirichlet boundary conditions and mixed delays
This section deals with obtaining sufficient conditions that guarantee the existence and global exponential stability of periodic solution for the system 2.1 - 2.2
Summary
Neural networks NNs with time delays have received considerable attention due to their extensive applications in solving some optimization problems, associative memory, classification of patterns, and other areas. In implementation of NNs, time delays are unavoidably encountered. It has been found that the existence of time delays may lead to instability and oscillation in a neural network. The analysis of the dynamical behaviors such as stability, periodic oscillation, and chaotic behavior are necessary work for practical design of delayed NNs 1–12. Zheng and Chen 1 studied the exponential stability for delayed periodic dynamical systems. In 2 , the global exponential stability and periodicity of a class of recurrent NNs with time delays are addressed by using Lyapunov functional method and inequality techniques. The diffusion phenomena could not be ignored in NNs when electrons are moving in asymmetric electromagnetic
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