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Hopf Bifurcation Analysis of Hyperhaotic Lorenz System

LIU Yongjian1,CHENG Junfang2 (1.School of Mathematics and Information Science,Yulin Normal University,Yulin 537000,China;2.School of Mathematics and Information Sciences,Henan University,Kaifeng 475004,China)  
In this paper,the Hopf bifurcation of a four-dimension(4D) Lorenz hyperchaotic system is investigated in detail.The conditions of the existence of Hopf bifurcation are given.Within normal form theory,complete mathematical characterizations for 4D Hopf bifurcation,including the direction of Hopf bifurcation,the stability of bifurcating period solutions and the expression of the bifurcating periodic solution are rigorous derived and studied.Finally,numerical simulations are performed to justify the theoretical analysis.
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