摘要
研究了一个分数阶离散Lorenz映射系统的动力学行为.首先研究了系统随不同参数变化的动力学行为,发现系统发生了周期倍分岔和Hopf分岔.然后为了进一步研究系统的动力学行为,基于数值模拟,得到了系统随参数和分数阶的阶数同时变化的三维分岔图.通过三维分岔图发现,该映射系统随着阶数的逐渐减小,动力学行为变得越来越简单,最后完全进入周期窗口;随着阶数逐渐增大,动力学行为变得越来越复杂.
The dynamics of a fractional-order discrete Lorenz system is studied.Firstly,dynamics of the system with different values of the system parameter was analyzed,and a series of period-doublings and Hopf bifurcations can be observed.Secondly,bifurcations for the system with the variation of a system parameter and a derivative order were investigated and presented in a three-dimensional space.The dynamics behavior of the system changes from chaos to regular with an decrease of derivative orders,and changes from regular to chaos with an increase of derivative orders.
作者
梁雪峰
刘晓君
LIANG Xuefeng;LIU Xiaojun(School of Mathematics and Statistics,Tianshui Normal University,Gansu Tianshui 741001,China;School of Sciences,Xi'an University of Posts and Telecommunications,Shaanxi Xi'an 710121,China)
出处
《河北师范大学学报（自然科学版）》
CAS
2022年第2期154-157,共4页
Journal of Hebei Normal University：Natural Science
基金
甘肃省高等学校创新基金(2020B-191)
天水师范学院2019年创新能力提升项目(CXT2019-23)。
关键词
离散分数阶系统
混沌
HOPF分岔
周期倍分岔
fractional-order discrete system
chaos
Hopf bifurcation
period-doubling bifurcation
