Global exponential stability of periodic solution for shunting inhibitory CNNs with delays

Anti-Periodic Solutions for Shunting Inhibitory Cellular Neural Networks with Time-Varying Coefficients

“…By applying techniques similar to those in [15], we establish new sufficient conditions ensuring the existence, uniqueness and exponential stability of anti-periodic solutions of system (1.1). Our results not only can be applied directly to many concrete examples of SICNNs, but also extend, to a certain extent, the results in [1][2][3][4][5][6][7][8][9]. Moreover, an example is provided to illustrate the effectiveness of our results.…”

“…Remark 4.1 One can observe thatall the results in [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] and the references therein can not be applicable to system (4.1) to obtain the existence and exponential stability of the anti-periodic solutions. Moreover, the results in [15] is the special case of Theorem 3.1 with a i j (t) ≡ a i j and C i j (t) ≡ C kl i j .…”

“…The applicability and efficiency of such networks hinge upon their dynamics, and therefore the analysis of dynamic behaviors of the networks is a first and necessary step for any practical design and application of the networks. Recently, considerable effort has been devoted to study dynamic behaviors, in particular, the existence and stability of the equilibrium point, periodic and almost periodic solutions of SICNNs with time-varying delays and continuously distributed delays in the literature (see, e.g., [4][5][6][7][8][9] and the references therein). As a result, a set of very generic, in-depth, criteria for the stability has been obtained for SICNNs.…”

Stability of shunting inhibitory cellular neural networks with unbounded time-varying delays

“…In particular, there have been extensive results on the problem of the existence and stability of the equilibrium points, and periodic and almost periodic solutions of SICNNs with time-varying delays in the literature. We refer the reader to [4][5][6][7] and the references cited therein. Suppose that there exists a constant τ such that…”

Existence and Exponential Stability of Almost Periodic Solution for Shunting Inhibitory Cellular Neural Networks With Distributed Delays and Large Impulses

“…For significance of almost periodicity, one also can refer to [8,11,23,24,27]. Li [13] obtained several sufficient conditions to ensure the global exponential stability of almost periodic solutions or periodic solutions for the delayed SICNNs. The criteria for the stability of almost periodic solutions of the SICNNs with distributed delays were given in [17,18,30].…”