Stability Analysis of Impulsive Stochastic Reaction-Diffusion Cellular Neural Network with Distributed Delay via Fixed Point Theory

Abstract

This paper investigates the stochastically exponential stability of reaction-diffusion impulsive stochastic cellular neural networks (CNN). The reaction-diffusion pulse stochastic system model characterizes the complexity of practical engineering and brings about mathematical difficulties, too. However, the difficulties have been overcome by constructing a new contraction mapping and an appropriate distance on a product space which is guaranteed to be a complete space. This is the first time to employ the fixed point theorem to derive the stability criterion of reaction-diffusion impulsive stochastic CNN with distributed time delays. Finally, an example is provided to illustrate the effectiveness of the proposed methods.

Boundedness and robust analysis of dynamics of nonlinear diffusion high-order Markovian jump time-delay system

“…Moreover, if the diffusion phenomenon is ignored, (4.1) degenerates into the following cellular neural network: To prove Theorem 4.3, we need to utilize [6,Thm. 5], to derive the following lemma.…”

“…Proof Rao and Zhong [6] utilized the Banach fixed point theorem, the Hölder inequality, the Burkhold-Davis-Gundy inequality, and the continuous semigroup of the Laplace operator to derive the globally stochastically exponential stability in mean square of the following impulsive stochastic reaction-diffusion cellular neural network with distributed delay:…”

“…All the time neural networks have attracted much attention for its wide application [1][2][3][4][5][6][7]. In 1983, Cohen-Grossberg neural networks (CGNNs) were originally proposed in [8].…”

Robust Stability of Nonlinear Diffusion Fuzzy Neural Networks with Parameter Uncertainties and Time Delays

“…In recent decades, reaction-diffusion neural networks have been the subject of research due to the fact that electrons have diffusion behaviors in an inhomogeneous magnetic field, and the role of diffusion items have always been investigated and discussed in many existing results ( [1][2][3][4]). Since the conduction velocity of electrons and components is limited, the phenomenon of time delays inevitably appears in various practical projects.…”

New Stability Criterion for Takagi‐Sugeno Fuzzy Cohen‐Grossberg Neural Networks with Probabilistic Time‐Varying Delays

“…But the success of these applications largely depends on whether the system has some stability, and so people began to be interested in the stability analysis of the system. In recent decades, reaction-diffusion neural networks have received much attention ( [7][8][9][10][11][12][13]), including various Laplacian diffusion ( [6,[14][15][16][17][18][19][20]). Besides, people are paying more and more attention to fuzzy neural network system ( [21][22][23][24][25][26][27][28][29][30][31][32][33][34]), due to encountering always some inconveniences such as the complicity, the uncertainty, and vagueness ( [27,[35][36][37]).…”