Cyclic symmetric dynamics in chaotic maps

Jin Liu, Kehui Sun and Huihai Wang

Chaos, Solitons & Fractals, 2024, vol. 189, issue P1

Abstract: In a recent paper (Liu et al., 2024), we reported on the microscopic mechanism underlying multistability in discrete dynamical systems, suggesting the potential for higher, even arbitrary-dimensional multistability in our conclusions. Before we can validate it, a fundamental question arises: what method can preserve the global dynamics of systems while allowing for an increase in dimensionality? This paper identifies the cyclic symmetric structure as a crucial solution and establishes two two-dimensional maps model based on it. The presence of multistability in any direction is affirmed, with this phenomenon representing either homogeneous or heterogeneous infinite expansion of the medium in multidimensional space. Furthermore, we uncover a range of dynamical characteristics, including grid-like phase trajectories, scale-free attractor clusters, fractal basin structures, symmetric attractors, and chaotic diffusion, all rooted in the system’s symmetric dynamical nature. This research not only enhances the comprehension of high-dimensional symmetric dynamics, but also offers a novel perspective for elucidating related models and phenomena.

Keywords: Chaotic map; Cyclic symmetric dynamics; Multistability (search for similar items in EconPapers)
Date: 2024
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077924012360
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:189:y:2024:i:p1:s0960077924012360

DOI: 10.1016/j.chaos.2024.115684

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().