Abstract
This paper deals with the exponential synchronization problem for reaction-diffusion neural networks with mixed time-varying delays and stochastic disturbance. By using stochastic analysis approaches and constructing a novel Lyapunov–Krasovskii functional, a periodically intermittent controller is first proposed to guarantee the exponential synchronization of reaction-diffusion neural networks with mixed time-varying delays and stochastic disturbance in terms of p-norm. The obtained synchronization results are easy to check and improve upon the existing ones. Particularly, the traditional assumptions on control width and time-varying delays are removed in this paper. This paper also presents two illustrative examples and uses simulated results of these examples to show the feasibility and effectiveness of the proposed scheme.
Highlights
In the past decade, there has been a great interest in various types of neural networks due to their wide range of applications, such as signal processing, pattern recognition, image processing, associative memory, fault diagnosis, aerospace, defense,c Vilnius University, 2014telecommunications, automatic control engineering, and combinatorial optimization
The organization of this paper is as follows: problem statement and preliminaries are presented; in Section 3, a periodically intermittent controller is proposed to ensure exponential synchronization of reaction-diffusion neural networks with mixed time-varying delays and stochastic noise perturbation in terms of p-norm; numerical simulations will be given in Section 4 to demonstrate the effectiveness and feasibility of our theoretical results
We introduce some notations, the notion of exponential synchronization for reaction-diffusion neural networks (1) and (4) under periodically intermittent controller (5) based on p-norm, and some lemmas, which will come into play later on
Summary
There has been a great interest in various types of neural networks (for example, Hopfield neural networks, cellular neural networks, Cohen–Grossberg neural networks, bidirectional associative memory neural networks, competitive neural networks, etc.) due to their wide range of applications, such as signal processing, pattern recognition, image processing, associative memory, fault diagnosis, aerospace, defense,. To the best of our knowledge, there are few results, or even no results concerning the synchronization issues for neural networks with mixed time-varying delays, stochastic noise perturbation and reaction-diffusion in terms of p-norm by using periodically intermittent control. Motivated by the above discussion, this paper is concerned with the exponential synchronization for reaction-diffusion neural networks with mixed time-varying delays and stochastic perturbation in terms of p-norm by using periodically intermittent control approach. The organization of this paper is as follows: problem statement and preliminaries are presented; in Section 3, a periodically intermittent controller is proposed to ensure exponential synchronization of reaction-diffusion neural networks with mixed time-varying delays and stochastic noise perturbation in terms of p-norm; numerical simulations will be given in Section 4 to demonstrate the effectiveness and feasibility of our theoretical results. Throughout this paper, Rn and Rn×m denote the n dimensional Euclidean space and the set of all n × m real matrices, respectively; the notation C 2,1(R+ × Rn; R+) denotes the family of all nonnegative functions V (t, x(t)) on R+×Rn, which are continuously twice differentiable in x and once differentiable in t; (Ω, F, P) is a complete probability space, where Ω is the sample space, F is the σ-algebra of subsets of the sample space and P is the probability measure on F; E{·} stands for the mathematical expectation operator with respect to the given probability measure P; “sgn” is the sign function
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call