Stability and dynamics of a stochastic discrete fractional-order chaotic system with short memory

IF 2.3 Q1 MATHEMATICS
Jie Ran, Jixiu Qiu, Yonghui Zhou
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Abstract

Abstract In this paper, a stochastic discrete fractional-order chaotic system with short memory is proposed, which possesses two equilibrium points. With the help of the Lyapunov function theory, some sufficient conditions for the stability in probability of the two equilibrium points are given. Secondly, the effects of fractional order and memory steps on the stability of the system are discussed. Finally, the path dynamical behavior of the system is investigated using numerical methods such as Lyapunov exponents, bifurcation diagram, phase diagram, and 0–1 test. The numerical simulation results validate the findings.

Abstract Image

具有短记忆的随机离散分数阶混沌系统的稳定性和动力学
摘要提出了一种具有两个平衡点的随机离散短记忆分数阶混沌系统。利用李雅普诺夫函数理论,给出了两个平衡点概率稳定的充分条件。其次,讨论了分数阶和记忆步长对系统稳定性的影响。最后,利用李雅普诺夫指数、分岔图、相图和0-1检验等数值方法研究了系统的路径动力学行为。数值模拟结果验证了上述结论。
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CiteScore
2.30
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0.00%
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