新五维超混沌Lorenz系统

A new five-dimensional hyperchaotic Lorenz system

通过加入线性和非线性状态反馈控制器的方法到三维Lorenz系统中,构造出了五维新超混沌Lorenz系统,详细研究了其动力学行为,包括平衡点的稳定性、随参数变化的分岔图、奇怪吸引子和李雅普诺夫指数谱等随参数范围变化关系.结果表明,新五维超混沌Lorenz系统具有较大的使系统处于超混沌状态的参数范围,且使系统处于混沌状态的参数范围极小,同时系统具有较宽的周期轨道和拟周期状态范围,动力学演化过程清晰明了.

A new five-dimensional hyperchaotic Lorenz system has been constructed by adding a linear feedback controller and a nonlinear feedback controller to the three-dimensional chaotic Lorenz system.The dynamic behaviors including the stability of equilibriums,the bifurcation diagram,strange attractors and Lyapunov exponents are studied when the system parameter ris varied in detail.The results of this study show the new five-dimensional hyperchaotic Lorenz system has a wide parameter range which makes the system in hyperchaos state and has very a narrow range that make the system in chaos state.The system also has a wide parameter range that make system in periodic orbit and quasi-periodic orbit.The process of the new system＇s behaviors is very obvious.