分数阶系统中不动点的稳定性与混沌

On stability of fixed points and chaos in fractional systems.

作者信息

Edelman Mark

机构信息

Department of Physics, Stern College at Yeshiva University, 245 Lexington Ave., New York, New York 10016, USA; Courant Institute of Mathematical Sciences, New York University, 251 Mercer St., New York, New York 10012, USA; and Department of Mathematics, BCC, CUNY, 2155 University Avenue, Bronx, New York 10453, USA.

出版信息

Chaos. 2018 Feb;28(2):023112. doi: 10.1063/1.5016437.

DOI:10.1063/1.5016437

PMID:29495677

Abstract

In this paper, we propose a method to calculate asymptotically period two sinks and define the range of stability of fixed points for a variety of discrete fractional systems of the order 0<α<2. The method is tested on various forms of fractional generalizations of the standard and logistic maps. Based on our analysis, we make a conjecture that chaos is impossible in the corresponding continuous fractional systems.

摘要

在本文中，我们提出了一种计算渐近周期二汇点的方法，并定义了0<α<2阶的各种离散分数系统的不动点稳定性范围。该方法在标准映射和逻辑斯谛映射的各种分数形式推广上进行了测试。基于我们的分析，我们推测在相应的连续分数系统中不可能出现混沌。