Stability Of Several Classes Of Delay Differential Equations And Impulsive Dynamic Equations On Time Scales

With the development of modern science and technology, people have proposed agreat many problems about differential and difference equations in natural science andsocial science, and some results are gained. The theory of time scales can unify continuousand discrete cases, which pioneers a new mathematical area. This theory not only unifiesdifferential and difference equations, reveals the essence of continuous and discrete cases,avoids repeat study, but also contains many other cases. The prominent peculiarity of timescales is unification and generalization, so the study of time scales has importantsignificance in theory and application. In addition, theory of dynamic equations on timescales has been proved to be of great importance and potential application as toembranchment of applied mathematic.This paper focuses on the research of stability behavior for dynamic equations andimpulsive dynamic systems on time scales.Firstly,32stability behavior for two classes of neutral delay dynamic equationswith positive and negative coefficients on time scales are studied in this paper. By usingthe basic theory of calculus on time scales and Gronwall's inequality and so on, somesufficient conditions for the uniformly stability and uniformly asymptotic stability of thesesystems with a direct method are gained.Secondly, in this paper the practical stability of dynamic systems with impulses atvariable times on time scales is considered. The measure function with the character ofLyapunov function is combined. Directly use two measure functionsh0,h its owncharacteristics to obtain some criteria for the practical stability in terms of two measures.At the same times, practical stability of a class of impulsive dynamic system in terms oftwo measures on time scales is considered.Finally, discuss eventual stability of a class of impulsive perturbed dynamic systemon time scales, we obtain some criteria of uniformly eventual stability and uniformlyeventual asymptotic stability in terms of two measures for the system are derived.