Inducing multistability in discrete chaotic systems using numerical integration with variable symmetry

Valerii Yu. Ostrovskii, Vyacheslav G. Rybin, Artur I. Karimov and Denis N. Butusov

Chaos, Solitons & Fractals, 2022, vol. 165, issue P1

Abstract: Multistability is an inherent property of many nonlinear dynamical systems. However, finding exact conditions where a certain nonlinear system is multistable, is a complex problem. In this study, we propose a novel approach for inducing multistability in a discrete system by applying the numerical integration method with variable symmetry to a continuous monostable system and finding a range of the symmetry coefficients for which multiple attractors coexist in its discrete model. We consider the well-known Chen system as an example, showing that multistability can be induced by discretization with variable symmetry. A special two-stage algorithm is proposed for a fast search for hidden attractors. Using the proposed algorithm, we found several multistable versions of the discrete Chen system and investigated their attractors and basins of attraction. By applying numerical backward error analysis, we discovered a generalized continuous Chen system with additional terms which were not present in the original system and have shown its approximate equivalence to the obtained discrete system. The results of this study can be used for inducing artificial multistability in a wide range of chaotic systems with possible applications in chaotic cryptography, communication, and chaos-based sensing.

Keywords: Chaos; Multistability; Variable symmetry; Artificial multistability; Bifurcation analysis; Backward error analysis (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077922009730
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:165:y:2022:i:p1:s0960077922009730

DOI: 10.1016/j.chaos.2022.112794

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. ().