分数阶混沌系统数值解析与电路仿真研究*

针对如何分析分数阶混沌系统的问题，基于改进的Adams-Bashforth-Moulton算法，研究了一个新三维分数阶混沌系统的数值解析方法，采用MATLAB软件平台，获得了该系统在不同分数阶时生成的混沌吸引子。基于频域近似法，采用RC串并联电路设计了分数阶单元电路，由一个模拟电路实现了所提出的分数阶混沌系统。电路仿真与数值解析结果一致，表明了所提出的两种分析方法是可行的，并证实了该分数阶混沌系统也有着复杂的非线性物理现象。

Numerical analysis and circuit simulation of fractional-order chaotic system

To analyze a fractional-order chaotic system, based on an improved version of Adams-Bashforth-Moulton algorithm, investigated the method of numerical analysis for a new three-dimensional fractional-order chaotic system and achieved chaotic attractors generated from this system with different fractional-order by utilizing MATLAB software platform. Then based on frequency-domain approximation algorithm, designed a fractional-order unit circuit with an RC serial-parallel circuit and realized the proposed fractional-order chaotic system by using an analogue circuit. These results from circuit simulation and numerical analysis are identical, which indicate that the proposed two methods are feasible and verify that there is also complex nonlinear physical phenomenon in the fractional-order chaotic system.