中文摘要：

研究四维超混沌Lorenz系统的Hopf分岔问题,给出系统存在Hopf分岔的条件,利用规范型理论,进一步研究系统Hopf分岔点的数学特性,包括分岔周期解、分岔周期解的周期、分岔周期解的分岔方向和稳定性等的数学表达式.最后借助数值模拟证实理论分析的正确性.

英文摘要：

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.