Hopf Bifurcation Analysis and Bifurcation Control of a Lorenz-Like System

Hopf bifurcation behavior and bifurcation control of a new Lorenz-like system are studied in this paper.Firstly,Hopf bifurcation type is determined by bifurcation stability norm.Then the linear controller and the non-linear controller are applied to control the original system respectively.In the section of linear control,the effect of linear parameter on the position of Hopf bifurcation is discussed by Routh-Hurwitz criterion;In the section of non-linear control,the Hopf bifurcation Normal Form of controlled system is obtained by using direct Normal Form method,and the effects of nonlinear parameter on amplitude of limit cycle and Hopf bifurcation type are discussed by coefficient of Normal Form.Discussions show that if non-linear parameter satisfies certain condition,bifurcation type of original system will be changed,and the periodic solution amplitude will increase with the parameter increasing.