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Anti-control of Hopf bifurcation in the new chaotic system with two stable node-foci

Authors
Journal
Applied Mathematics and Computation
0096-3003
Publisher
Elsevier
Publication Date
Volume
217
Issue
1
Identifiers
DOI: 10.1016/j.amc.2010.05.035
Keywords
  • Strange Chaotic Attractors
  • Control
  • Lyapunov Coefficient
  • Degenerate Hopf Bifurcation
  • Limit Cycles

Abstract

Abstract In order to further understand a complex 3D dynamical system showing strange chaotic attractors with two stable node-foci near Hopf bifurcation point, we propose nonlinear control scheme to the system and the controlled system, depending on five parameters, can exhibit codimension one, two, and three Hopf bifurcations in a much larger parameter regain. The control strategy used keeps the equilibrium structure of the chaotic system and can be applied to degenerate Hopf bifurcation at the desired location with preferred stability.

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