Stability of stochastic impulsive reaction–diffusion neural networks with S-type distributed delays and its application to image encryption

Abstract

In this paper, we study stochastic impulsive reaction-diffusion neural networks with S-type distributed delays, aiming to obtain the sufficient conditions for global exponential stability. First, an impulsive inequality involving infinite delay is introduced and the asymptotic behaviour of its solution is investigated by the truncation method. Then, global exponential stability in the mean-square sense of the stochastic impulsive reaction-diffusion system is studied by constructing a simple Lyapunov-Krasovskii functional where the S-type distributed delay is handled by the impulsive inequality. Numerical examples are also given to verify the effectiveness of the proposed results. Finally, the obtained theoretical results are successfully applied to an image encryption scheme based on bit-level permutation and the stochastic neural networks.

Stability Analysis of Nontrivial Stationary Solution and Constant Equilibrium Point of Reaction-Diffusion Neural Networks With Time Delays

“…There has always been a problem (see,e.g. Remark 8): whether is it the case in the literature( [1][2][3][4][5][6][7][8][9][10]) that the greater the diffusion, the more stable the system will be ? Now, our (3.35).…”

“…For a long time, the stability of the reaction diffusion neural networks was investigated in many literatures [1][2][3][4][5][6][7][8][9][10], in which the stability of the constant equilibrium point was studied. For example, in [1], the following cellular neural networks with time-varying delays and reaction-diffusion terms was considered, Here, we have to say, the equilibrium point y * is also the equilibrium point of the following ordinary differential equations corresponding to the time-delayed partial differential equations (1.1), dx(t) dt = − Cx(t) + Ag(x(t)) + Bg(x(t − τ(t))) + J, t ∈ R + , (1.3) Due to the Poincare inequality, we see, the diffusion items actually promote the stability of the reaction diffusion system (1.1).…”

Stability Analysis of Nontrivial Stationary Solution and Constant Equilibrium Point of Reaction-Diffusion Neural Networks with Time Delays under Dirichlet Zero Boundary Value

“…These wave propagation phenomena are exhibited by systems belonging to very different scientific disciplines. Besides, the interactions arising from the space-distributed structure of the multilayer cellular neural networks can be seen as diffusion phenomenon( [3,29]). Thereby, the reaction-diffusion effects cannot be neglected in both biological and man-made neural networks, especially when electrons are moving in non-even electromagnetic field.…”

pth Moment Stability of a Stationary Solution for a Reaction Diffusion System with Distributed Delays

“…It is well known that, in practical engineering, electrons inevitably diffuse in the inhomogeneous electromagnetic field. In addition, hence, the stability analysis of the reaction-diffusion system has become a hot topic [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. In recent decades, many authors, such as Linshan Wang, Qiankun Song and Jinde Cao, have studied the stability of Laplacian reaction-diffusion neural networks with time delay, and achieved fruitful results in Laplacian diffusion systems [7][8][9][10][11][12][13][14].…”