Periodic Solutions Of Several Perturbed Differential Equations

Impulsive differential system as a nonlinear differential system, is to describe some rapid change or jumping movement at fixed time or not fixed time. It can be more real reflect these movements. Its most outstanding characteristic is able to fully consider the im-pact of instantaneous change phenomenon of state and more accurately reflect the change law of things. In physics, electromagnetism, ecology population dynamics and many math-ematical models of economics are need to be expressed with it. It has important meaning in theory and practical life, so more and more attention from scholars.In this paper, we will research periodic solution of several a few classes differential equations with impulsive and its stability. One kind of systems which is as a prey-predator system use the continuous dependence of solution on parameters as well as the related theorem of differential equation to study its nature with the change of parameters. We prove the existence of the 1-order and k-order periodic solution and their stability. At last, we give the numerical simulations. Besides, we study the other system which can be as an eco-epidemiological model with impulsive perturbation. We prove its periodic solution is bounded at first, and then we study the periodic solution is permanence with the Floquet theory and the comparison theorem of impulsive differential equation.