Existence and stability of anti-periodic solutions for an impulsive Cohen-Grossberg SICNNs on time scales

S INCE Bouzerdout and Pinter in [1] described SICNNs as a new cellular neural networks, SICNNs have been extensively applied in psychophysics, perception, robotics, adaptive pattern recognition, vision and image processing, etc. It is shown that the applicability and efficiency of such networks hinge upon their dynamics, and therefore the analysis of dynamic behaviors is a preliminary step for any practical design and application of the networks. In particular, considerable effort has been devoted to the study of dynamic behaviors on 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., [2-5] and the references therein). Arising from problems in applied sciences, the existence of anti-periodic solutions plays a key role in characterizing the behavior of nonlinear differential equations (see [6-10]). Since SICNNs can be analog voltage transmission which is often an anti-periodic process, it is worth continuing the investigation of the existence and stability of anti-periodic solutions of SICNNs. To the best of the authors’ knowledge, nevertheless, there are few published papers considering the anti-periodic solutions of impulsive CGSICNNs. Motivated by all above mentioned, we consider the following impulsive CGSICNNs on time scales