Almost Automorphic Solutions For Shunting Inhibitory Cellular Neural Networks With Leakage Delays On Time Scales

In this thesis, shunting inhibitory cellular neural networks (SICNNs) with time-varying delays in the leakage term and continuously distributed delays on time scale T is proposed. Based on the exponential dichotomy of linear dynamic equation on time scales, fixed point theorems on time scales we obtain some new sufficient conditions for the existence an global exponential stability of almost automorphic solution for that class of neural networks. Moreover, we give convictive numerical examples to show the feasibility of our results. This thesis contains the several classes of Functional Differential Equations, including the existence of solutions and the stability of this solution on time scales. Also, some new results are obtained.A brief description of the organization of the thesis is as follows.In Chapter 1, we consider following shunting inhibitory cellular neural networks (SIC-NNs) model with time-varying delays in the leakage terms and continuously distributed delays on time scales T: where T is an almost time scale, t ∈ T.Vu G [0,+∞)T,t∈T have t-u ∈ T,tij(t) ∈ T, i= 1, ..., n, j= 1, ..., m. Based on the exponential dichotomy of linear dynamic equa-tion on time scales, fixed point theorems on time scales we obtain some new sufficient conditions for the existence an global exponential stability of almost automorphic solu-tion for this shunting inhibitory cellular neural networks (SICNNs). Moreover, we give convictive numerical examples to show the feasibility of our results.In Chapter 2, we consider following neutral shunting inhibitory cellular neural net-works(SICNNs)model with time-varying delays in the leakage terms and continuously distributed delays on time scales T: where t € T. For Vu € [0,+∞)T,t∈T have t-u ∈T,t-Tij∈ T, i= 1,..., n, j= 1, ...,m. By using the exponential dichotomy of linear dynamic equation on time s-cales, fixed point theorems on time scales we obtain some new sufficient conditions for the existence an global exponential stability of almost automorphic solution for this neu-tral shunting inhibitory cellular neural networks (SICNNs). Moreover, we give illustrate numerical examples to show the feasibility of our results.