分数阶超混沌Lorenz系统的数值求解及其动力学特性分析

Numerical solution and dynamics analysis of fractional-order hyperchaotic Lorenz system

采用预估—校正算法和Adomian分解算法求解分数阶超混沌Lorenz系统,并对比研究两种算法结果。从得到的吸引子和频谱结果来看,两种算法得到的结果比较一致,都可用于分数阶混沌系统数值求解。分析了系统的动力学特性和C0复杂度,实验结果表明分数阶Lorenz系统具有丰富的动力学特性,采用Adomian算法能够得到更小的系统产生混沌最小阶数,当参数变化时,系统的混沌范围更广。最后基于C0复杂度设计了一种有效的系统参数选取算法。为分数阶混沌系统应用提供了理论与实验基础。

This paper solved the fractional-order hyperchaotic Lorenz system by applying predictor-corrector algorithm（ PCA）and Adomian decomposition method（ ADM）,and compared their results. The phase diagrams and frequency spectrums obtained by the two algorithms are similar. It means that both algorithms can be employed to solve the fractional-order chaotic systems. This paper analyzed the dynamics and C0 complexity of the system,and the results show that the fractional-order hyperchaotic Lorenz system has rich dynamical behaviors. The minimum order to generate chaos based on PCA is smaller than that based on ADM. Meanwhile,the parameter range to generate chaos is wider by ADM when the parameter varies. Finally,this paper proposed an effective parameter choice scheme based on C0 complexity. It provides the theoretical and experimental basis for the application of fractional-order chaotic system.