 Self-excited and hidden attractors in a multistable jerk systemPaulo C. Rech Chaos, Solitons & Fractals, 2022, vol. 164, issue C Abstract: In this paper we investigate a jerk system which is modeled by a homogeneous third-order ordinary differential equation, with four parameters that control the dynamics. The proper choice of one of these parameters allows the system to display real or non-real equilibrium points. This implies that we can choose such a parameter so that the associated attractors are either self-excited or hidden. We consider the two situations, and investigate the dynamics of the two versions of this jerk system, in cross-sections of the three-dimensional parameter-space generated by the other three parameters. We show that both versions of the jerk system display multistability, with coexistence of periodic–periodic, chaotic–chaotic, and periodic–chaotic attractors in the phase-space, regardless of whether the attractors are self-excited or hidden. We also show that basins of attraction and attractors occupy smaller volumes in the case of the system with no equilibrium points. Keywords: Multistability; Hidden attractor; Self-excited attractor; Lyapunov exponents (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:164:y:2022:i:c:s0960077922007986 DOI: 10.1016/j.chaos.2022.112614 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 |
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