2010•Journal of Jiaying UniversityRequires access

The Bifurcation Analysis of One Disc Rete-time System

Huiqing Huang

Abstract

In this thesis,we discuss the complex dynamics of the two-dimensional discrete system as the bifurcation parameters are changed by using bifurcation theories in dynamical systems. We find the two-dimensional discrete system existence for pitchfork bifurcation,flip bifurcation and Hopf bifurcation are derived by using center manifold theorem and bifurcation theory.

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Key concepts: Pitchfork bifurcation, Bogdanov–Takens bifurcation, Transcritical bifurcation, Saddle-node bifurcation, Biological applications of bifurcation theory, Bifurcation diagram, Homoclinic bifurcation, Period-doubling bifurcation