Almost periodic solution of shunting inhibitory cellular neural networks with time varying and continuously distributed delays

Abstract

For shunting inhibitory cellular neural networks (SICNNs) with time varying, and continuously distributed, delays, by the investigation of the hull equation, this Letter gives several sufficient conditions guaranteeing the local existence, uniqueness and uniform asymptotical stability of one almost periodic solution of the networks using inequality techniques, fixed point theory and Lyapunov functional. Compared with some known results, the obtained ones are less restrictive, e.g., the assumptions requiring the absolute value of the activation functions to be bounded, and the kernel functions k i j ( s ) , determining the distributed delays, to be ∫ 0 ∞ k i j ( s ) exp ( λ 0 s ) d s < ∞ ( λ 0 > 0 ), are completely dropped. Strictly speaking, all known results are not applicable to SICNNs with time varying coefficients, even for some SICNNs with constant coefficients, only our criterions can give explicit avouchment. Thus the obtained conclusions have wider applicable range, improve and complement the known results. Finally, the feasibility as well as the excellence is presented by two illustrative examples, respectively.