The Analysis Of Bifurcation Of A Economic Model

Based on a comprehensive analysis of complex dynamic systems and examination of the history and the actuality of the bifurcation and chaos research, a systematic investigation into the bifurcation and chaos control is made with the ordinary mathematic theory. Some important achievements are obtained in this dissertation. The whole paper consists of four chapters. Chapter 1 is an introduction of the dissertation. The importance of the research of the bifurcation is introduction, the advances and actuality of the research are summarized, and the main contents of the dissertation are reported as well. Chapter 2 is the summary of bifurcation, first it is introduction the summary of bifurcation of the discrete system, Secondly, it deals with the codem-1 bifurcation theory, the conditions giving rise to the static bifurcation, including transcritical bifurcation, fold bifurcation, and pitch-fork bifurcation etc. are derived. The end is introduction the codem-2 bifurcation theory, including three strong resonance: 1:2 resonance, 1:3 resonance, and 1:4 resonance. Chapter 3 analyzes the dynamical of a economic model in detail, mainly about codem-1 bifurcation and codem-2 bifurcation. Chapter 4 is the summary and conclusion of the dissertation.