Stability Of Dynamic Systems On Time Scales

Stability is one of the most fundamental issue. In the investigation of dynamic sys-tems, the comparison principle is important to discuss the stability of solutions. When consider the stability theory, or considered the theory of continuous, or discrete be con-sidered in isolation. In real life is often the coexistence between the two. however. To unify the theory of continuous and discrete dynamic systems, in 1988. Hilger proposed the study of dynamic systems on time scales and developed necessary calculus for functions on time scales. The paper is composed of five chapters.In Chapter 1, the history of the study about stability of dynamic system on time scales is introduced accompanied with some prints of present work as well as the main work of the paper.In Chapter 2, basic notions connected to time scales are given, the calculus on time scales related fundamental properties and the comparison principle on time scales are also presented.In Chapter 3, this Chapter studies some criteria results of x-stability of dynamic system and Lipschitz stability of impulsive dynamic system stability via cone-valued Lya-punov function and comparison principle on time scales.In Chapter 4, by using a notion of upper quasi-monotone nondecreasing. this Chapter give a new comparison principle which connects the solutions of two higher-dimensional dynamic systems on time scales. Then the stability criteria of solution of dynamic system on times in terms of two measures are obtained.In Chapter 5, an attempt for dynamic system is to offer sufficient conditions which weaker than usual to obtain boundedness criteria.