Stability Analysis For Several Types Of Impulsive Dynamic Systems And Neural Networks With Time Delays On Time Scales

The theory of time scales can unify continuous and discrete cases, which pioneers anew mathematical area. This theory not only unifies differential and difference equations,reveals the essence of continuous and discrete cases, avoids repeat study, but also containsmany other cases. The prominent peculiarity of time scales is unification andgeneralization, so the study of time scales has important significance in theory andapplication. In addition, stability of dynamic equations on time scales has an extremelywide foundation of practical application, such as the spread of the epidemic model, theneural network model and the number of insects model are involved in stability problems.Therefore, the research on this subject can be more directly solve practical problems.In this paper, the practical stability and strict practical stability of impulsive dynamicsystems on time scales, stability for two types of time-delay neural networks on timescales have been studied respectively.Firstly practical stability of impulsive dynamic systems with initial time difference ontime scales is discussed in this paper, and some sufficient conditions to satisfy practicalstability and practical asymptotic stabllity of the systems are gained. At the same time, anexample is given to illustrate.Secondly practical stability for impulsive hybird dynamic systems with two measureson time scales is considered, and practical asymptotic stability criteria for the systems areobtained by employing multiple Lyapunov function method. Meanwhile, an example isshown to verify.Then still direct to the impulsive hybird dynamic systems on time scales, which strictpractical stability with two measures is studied, and the sufficient conditions for strictpractical stability and strict practical asymptotic stability are given by using comparisonsystem method.And then, the exponential stability for a class of finite time-delay Cohen-Grossbergneural networks on time scales is disscussed by using Lypunov function method andanalytical technique. And according to the Brouwer fixed point theorem, the sufficientconditions for existence of the equilibrium point is gained.Finally, the bi-directional associative memory neural networks with finite time delayson time scales have been researched, and sufficient condition for the global asymptoticstability of the equilibrium point is given by Lyapunov function method and Barblat theorem.