一种新的分数阶三维自治混沌系统

A Novel Fractional-order Three Dimensional Automation Chaotic System

提出了一种新的分数阶三维自治混沌系统.在研究了其平衡点,稳定性等基本特性的基础上给出了该系统的横向靠右的蝴蝶状奇怪吸引子.为了深入研究其复杂的奇怪吸引子的形成机制,提出了一种新的控制方法,并详细分析了控制变量在一定范围内变化时系统呈现的特定规律.而且还在此基础上提出了一种使系统收敛到其中一个平衡点的控制方法,该方法操作简单,且调节时间可以实现人为控制,并指出系统状态变量的调整时间随着控制变量的绝对值的增加不断缩短,仿真结果证明了这种方法的高效性.

The paper presents a novel fractional-order three dimensional automation chaotic system. Some basic properties, such as stability about the fractional-order nonlinear system, equilibrium points, the chaotic behaviors of transverse butterfly-shaped strange attractor to rightward have been studied. At the same time, the forming mech- anism of its compound strange attractor has been investigated, and the principles have been analysed when the con- trol variables vary in specific ranges. Based on the knowledge before, the paper proposes a controller to let the sys- tem converge to one of the equilibrium points, whose adjustment time can be changed easily. The adjustment time is related to the values of control variables. Numerical simulations prove the effectiveness of the controller.