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Theory of Bifurcations

  • G. C. Layek
Chapter

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 point. The behavior of fixed point and the nature of trajectories may change dramatically at bifurcation points. The characters of attractor and repellor 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 diagram. This chapter deals with important bifurcations of one and two-dimensional systems, their mathematical theories, and some physical applications.

Keywords

Equilibrium Point Rayleigh Number Lorenz System Pitchfork Bifurcation Stable Node 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer India 2015

Authors and Affiliations

  1. 1.Department of MathematicsThe University of BurdwanBardhamanIndia

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