Dynamic Analysis Of A Class Of Piecewise Maps With Discontinuous Points

In this paper,we ma inly study the dynamic behavior of a class of piecewise map with discontinuous points.Such piecewise map make the dynamic behavior richer due to the increase of the number of discontinuous points.In the first chapter,we first introduce the research background and the problems of this paper,then elaborate some definitions that need to be used in the paper,finally,we give the main research results and main structure of this paper.The second chapter,we study a piecewise linear map with one discontinuous point,with the same symbol of intercept and have a repulsive fixed point.For the map system,Firstly,a preliminary classification of the parameters is given.Then dynamical behavior of each case was analyzed.BCB bifurcation,flip bifurcation,contact bifurcation and chaos phenomenon,coexistence attractors basin delimitation and bifurcation of attractors were presented.At last,numerical simulation was used to verify the theoretical results.The third chapter,we discuss a piecewise nonlinear map with a discontinuous point and same symbol of intercept.Because the map system is highly similar to the second chapter,it can use the same way to analyze the dynamic behavior of the map system,through the analysis,shows existence of fold bifurcation,and other dynamic behavior is similar to the second chapter.The fourth chapter,we consider a piecewise linear map with two discontinuous points,with the same symbol of intercept and have a repulsive fixed point.Because the number of discontinuous points increases,the map may be have an area that can not be iteratively arrived,we call the forbidden area.According to the BCB definition,the influence of the number of discontinuous points on the dynamic behavior of the map is mainly reflected on BCB.This part will analysis the influence of the number of discontinuous points on the dynamic behavior of the map system.At last,we make a summary of this paper.