Bifurcation Of Nonlinear Dynamical Systems

Based on a complete summary 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 imp- ortant achievements are obtained in this dissertation.The whole paper consists of six chapters.Chapter 1 is an introduction of the disser- tation.The importance of the research of the bifurcation and chaos is introduced, the ad- vances and actuality of the research are summarized, and the main contents of the disse- rtation are reported as well. Chapter 2 deals with the fundamental theory. The conditions giving rise to the static bifurcation ,including transcritical bifurcation, fold bifurcation , and pitchfork bifurcation etc. are derived. At the same time,several important chaotic at- tractors are introduced. Chapter 3 analyzes the dynamical behavior of a chemical model . The condition giving rise to Hopf bifurcation is derived and the global dynamics is des- cribed. In chapter 4 , several main bifurcations of Kopel system are studied in detail. In chapter 5,chaos control of Lu system is investigated. The results show chaotic attractor of Lu system can be controlled at an equilibrium or a periodic orbit. Chapter 6 is the summary and conclusion of the dissertation.