一类新的四维超混沌系统及其动力学分析

A Novel Four-dimensinal Hyperchaotic System and Its Dynamic Analysis

为产生更复杂的超混沌吸引子,在经典Lv混沌系统基础上增加一维状态和2个参数,构建了一类新的四维超混沌系统.理论分析了新系统的对称性、耗散性、吸引子的存在性和平衡点的稳定性.利用数值模拟方法分析了新系统的相图、分岔图、Lyapunov指数谱和Lyapunov维数.结果表明,新系统在新引入的2个参数控制下分别具有相同的复杂动力学行为,分别运行于超混沌、混沌、拟周期和周期等不同轨道状态.

In order to generate more complex hyperchaotic attractor,a new four-dimensinal hyperchaotic system is constructed by adding an additional state and two parameters to the classic Lv chaotic system.The symmetry,dissipation,the existence of attractor,stability of equilibrium points of the new system are analyzed theoretically.The phase diagram,bifurcation diagram and Lyapunov exponents spectrum and fractal dimension of the system are analyzed by means of numerical simulations.Results show that the new system has the same and complex dynamic behavior under the new introduced two parameters control respectively,which can run into hyperchaotic,chaotic,quasi-periodic and periodic orbits.