Attraction Of Li-Yorke Chaos By Hopfield Neural Networks Systems With Delays On Time Scales

In this thesis, we consider the following Hopfield-type neural networks of neutral-type with time-varying delays on time scales: satisfying the initial conditions: is a bounded delta derivative function, for each i=1,2,…,m,j=1,2,…,n.Based on the exponential dichotomy of linear dynamic equations on time scales, Banach’s fixed point theorem and the theory of calculus on time scales, and by using the scaling and simplification to the inequation, some sufficient conditions are obtained for the existence of chaos in dynamic equations on time scales. The results of the present study are based on the Li-Yorke definition of chaos. The results of this paper are completely new and complementary to the previously known results even in cases of the time scale T=R or T=Z. Finally, we present an example to illustrate our results are effective.