The Expansion And Further Study Of Impulsive Semidynamical Systems

In this paper, we improved impulsive semidynamical system which studied by E. M. Bonotto and M. Federson and others. We defined a more general impulse system in the premise of the initial point that can be the impulsive point and there are intersections between the impulsive set and the image set, which is called impulsive semidynamical systems of continuous jumping. We studied the new system in four aspects. Firstly, we presented its definition; Secondly, we presented the classifications and the descriptions of its impulsive trajectory; Thirdly, we discussed its limit set andπ-invariant; Finally, we studied its periodic solution and we gave two examples about periodic solution.