摘要
The anti-control of bifurcation refers to the task of creating a certain bifurcation with particular desired properties and location by appropriate controls. We consider, via feedback control and symbolic computation, the problem of anti-control of Hopf bifurcation in the chaotic Liu system. We propose an anti-control scheme and show that compared with the uncontrolled system, the anti-controlled Liu system can exhibit Hopf bifurcation in a much larger parameter region. The anti-control strategy used keeps the equilibrium structure of the Liu system and can be applied to generate Hopf bifurcation at the desired location with preferred stability. We illustrate the etticiency of the anti-control approach under different operating conditions.
The anti-control of bifurcation refers to the task of creating a certain bifurcation with particular desired properties and location by appropriate controls. We consider, via feedback control and symbolic computation, the problem of anti-control of Hopf bifurcation in the chaotic Liu system. We propose an anti-control scheme and show that compared with the uncontrolled system, the anti-controlled Liu system can exhibit Hopf bifurcation in a much larger parameter region. The anti-control strategy used keeps the equilibrium structure of the Liu system and can be applied to generate Hopf bifurcation at the desired location with preferred stability. We illustrate the etticiency of the anti-control approach under different operating conditions.
基金
Supported by the National Natural Science Foundation of China under Grant Nos 60772023 and 10432010.
