Periodic Solutions And Existence Of Chaos In Discrete Map Of Financial Systems

There are many untouched areas in the study of piecewise discontinuous map.This thesis mainly studies the dynamical behavior of piecewise discontinuous map,which aims to help people to understand the internal change rule of financial market and enrich the knowledge content of dynamics.In chapter 1,we introduce the research background and the problems of this thesis firstly,then we state some definitions that need to be used in this thesis,finally,we give the structure of this thesis.In chapter 2,we introduce the establishment process of the model to be studied in this thesis.In chapter 3,we analyzed the n-dimensional discontinuous map model of a financial market.According to the method that used by Dutta,we analyze the n-dimensional discontinuous map model of the financial market and obtain the general conditions for the existence of period-1 and period-2 orbits.Finally,we take a specific three-dimensional financial market model as an example to illustrate the application process of this method.In Chapter 4,we analyze the dynamical behavior of the two-dimensional discontinuous area-preserving map model of the financial market.At first,we focus on the general properties of the two-dimensional map,the types of fixed points of the map are shown,and the conditions for the existence of periodic saddle orbits are given.Next,we prove that non-smooth discontinuous area-preserving(NSDAP)map in the financial market exists homoclinic chaos for some parameter settings.Finally,we discuss the existence of a chaotic invariant saddle of the non-smooth discontinuous area-preserving(NSDAP)map.Finally,we make a summary of this thesis.