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Hopf Bifurcation Analysis and Control of a New Lorenz-like System

Zhang Zhonghua  
【摘要】:this paper is concerned with Hopf bifurcation behavior and bifurcation control of a new Lorenz-like system.Firstly,Hopf bifurcation type is studied based on the bifurcation stability norm,furthermore bifurcation period and characteristic exponent of system are given.Then the linear controller and the non-linear controller are applied to control the Hopf bifurcation of original system respectively.For linear control,the Routh-Hurwitz criterion is adopted to give parameter conditions making Hopf bifurcation dissapear;For non-linear control,the Hopf bifurcation Normal Form of controlled system is obtained by using the direct Normal Form method,besides,according to coefficient of Normal Form,the impact of selection criteria of non-linear parameter on amplitude of limit cycle and Hopf bifurcation type are discussed,discussions show that when the non-linear parameter satisfies certain condition,bifurcation type of original system will be changed,and the periodic solution amplitude will be changed with the parameter.Finally,theoretical results are verified by numerical simulations.

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