A shunting inhibitory cellular neural network with continuously distributed delays of neutral type

Neutral impulsive shunting inhibitory cellular neural networks with time-varying coefficients and leakage delays

“…The dynamics of a cell C ij are described by the following nonlinear ordinary differential equation: In a recent paper, Li et al (2012) considered the following SICNN with continuously distributed delays of neutral type: Inspired by these works, in this paper we consider the following impulsive shunting inhibitory cellular neural networks with time-varying coefficients and leakage delays of neutral type (NISICNN): …”

On Antiperiodic Solutions for Cohen-Grossberg Shunting Inhibitory Neural Networks with Time-Varying Delays and Impulses

“…Since all of these applications closely depend on their dynamics, the dynamical behaviors of SICNNs with delays have been widely studied (see Chen & Zhao, 2008;Fan & Shao, 2010;Li, Fang, & Yang, 2012;Li, Liu, & Zhu, 2005;Li & Wang, 2012;Liu, 2007;Liu, 2009c;Liu, You, & Cao, 2007;Zhao & Zhang, 2008). In applied sciences, the existence of antiperiodic solutions plays a key role in characterizing the behavior of nonlinear differential equations (Fan, Wang, & Yi, 2009;Li, Xu, & Zhang, 2010;Li & Yang, 2009;Shao, 2008).…”

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

“…By using Lyapunov functional method and differential inequality techniques, in [20], some sufficient conditions have been established to guarantee that all solutions of (1) converge exponentially to the almost periodic solution. Moreover, it is well known that the global exponential convergence behavior of solutions plays a key role in characterizing the behavior of dynamical system since the exponential convergent rate can be unveiled (see [21][22][23][24]). However, to the best of our knowledge, few authors have considered the exponential convergence on the pseudo almost periodic solution for (1).…”

“…Then, [19,20], the authors obtained the existence of almost periodic solution of SICNNs with leakage delays, but they did not give the existence and global exponential convergence for the pseudo almost periodic solution. Since [1][2][3][4][5][6][7][8][9] only dealt with SICNNs without leakage delays, [14][15][16][17][18][21][22][23][24] give no opinions about the problem of pseudo almost periodic solutions for SICNNs with leakage delays. One can observe that all the results in these literatures and the references therein cannot be applicable to prove the existence and exponential stability of pseudo almost periodic solutions for SICNNs (56).…”