On The Time Scale Impulsive Dynamical System

The theory of time scales, which has recently received a lot of attention, was introduced by Hilger in his Ph.D.Thesis in 1988 in order to integrate continuous and discrete analysis. But the work to study the dynamics of impulsive dynamic system on time scales, as the stability, periodicity and oscillation, rarely appeared. In this paper, based on the classic results of theory, we mainly consider the stability, periodicity and oscillation for several kind of impulsive dynamic system on time scales, which has the certain theory significance. This thesis is composed of five chapters.In the first chapters, we summarize the history of time scales, the existed related work and the origin of the problems we discussed. And the main works of this paper are also simply introduced.In the second chapter, we state simply some basic theories of time scales, including some related concepts and qualities.In the third chapter, we discuss the stability of impulsive dynamic system on time scales. By using the calculus and the Lyapunov function method, the uniform stability and uniform asymptotic stability criteria for this impulsive system on time scales are obtained, respectively.In the fourth chapter, we discuss the existence of periodic solutions for an impulsive system on time scales. By using the fixed theory , the existence theory of periodic solutions are obtained.Finally, in the fifth chapter, we study the oscillation for a second-order impulsive system on time scales.By using perfect square technology and parameter function, the oscillation criteria for this impulsive system are obtained.