The Stability For Two Class Of Delay Differential Dynamics On Time Scales

The theory of time scales, which has recently received a lot of attention, wasintroduced by Hilger in his Ph.D.Thesis in 1988 in order to uniform continuousand discrete analysis. But few studies consider the functional differential equationby the theory of time scales. In this paper, based on the classic results of stabilitytheory, we mainly consider the stability and convergence of two class delay dif-ferential systems on time scales,which extend and improve known results. Thisthesis is composed of four chapters.In the first chapter, we summarize the history of time scales, the existedrelated work and the origin of the problems we discussed. And the main works ofthis paper are also simply introduced.In the second chapter, in order to help us to understand this paper, we statesimply basic theories of time scales.In the third chapter, we discuss the uniformly stability and convergence of thedifferential system with finite variable delay on time scales. By using the calculusand some dynamic inequalities on time scales, we apply a direct method to obtainsufficient conditions for the uniformly stability and convergence of this system.And these results on time scales also conform with corresponding known resultsfor the differential equation and difference equation.Finally, in the fourth chapter, we study the uniformly stability and uniformlyasymptotic stability for a nonautonomous differential equation with delay. Byusing the comparison theorem and Gronwall inequality and so on, we obtain somecriteria of the uniformly stability and uniformly asymptotic stability for this systemwith a direct method, which also conform with corresponding known results forthe differential equation and difference equation and improve known results.