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Theory of Bifurcations

In: An Introduction to Dynamical Systems and Chaos

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  • G. C. Layek

    (The University of Burdwan, Department of Mathematics)

Abstract

Bifurcation means a structural change in the orbit of a system. The bifurcation of a system had been first reported by the French mathematician Henri Poincaré in his work. The study of bifurcation is concerned with how the structural change occurs when the parameter(s) are changing. The structural change and the transition behavior of a system are the central part of dynamical evolution. The point at which bifurcation occurs is known as the bifurcation pointBifurcation point . The behavior of fixed point and the nature of trajectories may change dramatically at bifurcation points. The characters of attractorAttractor and repellorRepellor are altered, in general when bifurcation occurs. The diagram of the parameter values versus the fixed points of the system is known as the bifurcation diagramBifurcation diagram . This chapter deals with important bifurcations of one and two-dimensional systems, their mathematical theories, and some physical applications.

Suggested Citation

  • G. C. Layek, 2015. "Theory of Bifurcations," Springer Books, in: An Introduction to Dynamical Systems and Chaos, chapter 0, pages 203-254, Springer.
    • Handle: RePEc:spr:sprchp:978-81-322-2556-0_6
    DOI: 10.1007/978-81-322-2556-0_6
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