A novel variable-order fractional chaotic map and its dynamics

doi:10.1088/1674-1056/ad1a93

Abstract In recent years, fractional-order chaotic maps have been paid more attention in publications because of the memory effect. This paper presents a novel variable-order fractional sine map (VFSM) based on the discrete fractional calculus. Specially, the order is defined as an iterative function that incorporates the current state of the system. By analyzing phase diagrams, time sequences, bifurcations, Lyapunov exponents and fuzzy entropy complexity, the dynamics of the proposed map are investigated comparing with the constant-order fractional sine map. The results reveal that the variable order has a good effect on improving the chaotic performance, and it enlarges the range of available parameter values as well as reduces non-chaotic windows. Multiple coexisting attractors also enrich the dynamics of VFSM and prove its sensitivity to initial values. Moreover, the sequence generated by the proposed map passes the statistical test for pseudorandom number and shows strong robustness to parameter estimation, which proves the potential applications in the field of information security.

Keywords: chaos fractional difference variable order multistability complexity

Received: 21 November 2023
Revised: 27 December 2023
Accepted manuscript online: 04 January 2024

PACS:	05.45.Ac	(Low-dimensional chaos)
	05.45.Pq	(Numerical simulations of chaotic systems)
	05.45.Tp	(Time series analysis)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 62071496, 61901530, and 62061008) and the Natural Science Foundation of Hunan Province of China (Grant No. 2020JJ5767).

Corresponding Authors: Huihai Wang
E-mail: wanghuihai_csu@csu.edu.cn

Cite this article:

Zhouqing Tang(唐周青), Shaobo He(贺少波), Huihai Wang(王会海), Kehui Sun(孙克辉), Zhao Yao(姚昭), and Xianming Wu(吴先明) A novel variable-order fractional chaotic map and its dynamics 2024 Chin. Phys. B 33 030503

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