新分数阶jerk混沌系统的有效数值模拟  

Effective Numerical Simulation of New Fractional-order Chaotic jerk System

作　　者：袁满玉 李浓森 李文渊 崔继峰[1] Yuan Manyu;Li Nongsen;Li Wenyuan;Cui Jifeng(College of Science,Inner Mongolia University of Technology,Hohhot 010051,China)

机构地区：[1]内蒙古工业大学理学院,呼和浩特010051

出　　处：《动力学与控制学报》2025年第2期10-16,共7页Journal of Dynamics and Control

基　　金：国家自然科学基金资助项目(12062018,12172333);内蒙古自治区高等学校青年科技英才支持计划资助项目(NJYT22075);内蒙古自治区直属高校基本科研业务费(JY20220063,JY20220331)。

摘　　要：目前大多采用预测校正法来计算分数阶动力系统,其它数值方法使用较少.本文利用拉格朗日多项式插值,详细阐述了一种用于计算分数阶动力系统的数值方法.并利用此方法成功获得了新分数阶jerk混沌系统的有效数值解,所得结果与预测校正法的结果进行对比,发现两者十分吻合,验证了方法的有效性.进一步探讨了新分数阶jerk混沌系统在不同系统阶数α下的最大Lyapunov指数,得出当系统阶数α=0.85、α=0.95时,系统不稳定,进一步展示了在Caputo意义下的系统相图.研究结果表明,不同的系统阶数α对新分数阶jerk混沌系统的动力学行为有显著影响.Most of the current research methods use the prediction correction method,but other numerical methods are less frequently used.In this paper,a numerical method for computing fractional-order dynamical systems is elaborated using Lagrange polynomial interpolation.This is used to successfully obtain an effective numerical solution for a new fractional-order jerk chaotic system.The results obtained are compared with those of the prediction correction method and found to be in good agreement with each other,verifying the validity of this method.The maximum Lyapunov exponent of the new fractional-order jerk chaotic system is further explored for different system orders,and it is concluded that the system exhibits instability when the system orderα=0.85,α=0.95,and the phase diagram of the system in Caputo’s sense is further demonstrated.The results show that different system orderαhave a significant effect on the dynamical behaviour of new fractional-order jerk chaotic system.

关 键 词：新分数阶jerk混沌系统 数值模拟 稳定性 动力学行为 

分 类 号：O193[理学—数学]