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Wei, Zhouchao; Yang, Qigui

Anti-control of Hopf bifurcation in the new chaotic system with two stable node-foci. (English) Zbl 1200.65102

Appl. Math. Comput. 217, No. 1, 422-429 (2010).
Summary: 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.

Cited in 54 Documents

MSC:

65P20 Numerical chaos
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37M20 Computational methods for bifurcation problems in dynamical systems
37G15 Bifurcations of limit cycles and periodic orbits in dynamical systems

Keywords:

strange chaotic attractors; control; Lyapunov coefficient; degenerate Hopf bifurcation; limit cycles; numerical examples
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\textit{Z. Wei} and \textit{Q. Yang}, Appl. Math. Comput. 217, No. 1, 422--429 (2010; Zbl 1200.65102)
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