Global Exponential Stability of Pseudo Almost Periodic Solutions for SICNNs with Time-Varying Leakage Delays

Abstract

This paper is concerned with the shunting inhibitory cellular neural networks (SICNNs) with time-varying delays in the leakage (or forgetting) terms. Under proper conditions, we employ a novel argument to establish a criterion on the global exponential stability of pseudo almost periodic solutions by using Lyapunov functional method and differential inequality techniques. We also provide numerical simulations to support the theoretical result.

Pseudo almost periodic solutions for CNNs with leakage delays and complex deviating arguments

“…The functions h and u in above definition are, respectively, called the almost periodic component and the ergodic perturbation of the pseudo almost periodic function f. The decomposition given in definition above is unique. Observe that ðPAPðR; R n Þ; : k k 1 Þ is a Banach space and APðR; R n Þ is a proper subspace of PAPðR; R n Þ since the function /ðtÞ ¼ cospt þ cost þ e Àt 4 sin 2 t is pseudo almost periodic, but not almost periodic [15].…”

“…We also mention that all results in the references [12][13][14][15][16] and [17,18] cannot be applied to imply the existence of pseudo almost periodic solutions of (4.1). Here, we employ a novel proof to establish some criteria to guarantee the existence of pseudo almost periodic solutions for CNNs with leakage delays and complex deviating arguments.…”

“…In the past four decades, people have paid much attention to the problem on almost periodic solutions and pseudo almost periodic solutions for cellular neural networks (CNNs) with leakage delays because of its successful applications in variety of areas such as signal processing, pattern recognition, chemical processes, nuclear reactors, biological systems, static image processing, associative memories, optimization problems and so on (see [12][13][14][15][16] and the references cited therein).…”

Pseudo Almost Periodic Solutions for SICNNs with Leakage Delays and Complex Deviating Arguments

“…Such time delays in the leakage term are difficult to handle but has great impact on the dynamical behavior of shunting inhibitory cellular neural networks (SICNNs). Therefore, people have paid much attention to the problem on almost periodic solutions and pseudo almost periodic solutions for SICNNs with leakage delays because of its successful applications in variety of areas such as psychophysics, speech, perception, robotics, adaptive pattern recognition, vision, and image processing (see [6][7][8] and the references therein).…”

New results on the stability of fuzzy cellular neural networks with time-varying leakage delays

“…Remark 4.1 It is worth noting that various fuzzy neural networks model with or without constant leakage delay were investigated by many authors [17,[19][20][21][22][24][25][26][27][28][29], to the best of our knowledge; however, the case with timevarying leakage delay for this model are seldom considered in the literature, and the method used here is different from these literatures. Moreover, the method in this present paper can be used to study on the stability of FCNNs with Continuously distributed leakage delays and the other types of FCNNS with leakage delays such as fuzzy shunting inhibitory cellular neural network and fuzzy CohenGrossberg neural networks.…”