A hidden chaotic attractor in the classical Lorenz system

Buncha Munmuangsaen and Banlue Srisuchinwong

Chaos, Solitons & Fractals, 2018, vol. 107, issue C, 61-66

Abstract: Chaotic attractors in the classical Lorenz system have long been known as self-excited attractors. This paper, for the first time, reveals a novel hidden chaotic attractor in the classical Lorenz system. Either a self-excited or a hidden chaotic attractor is now possible in the classical Lorenz system depending on values of both system parameters and initial conditions. A systematically exhaustive computer search is employed to directly search for the hidden chaotic attractor with elegant values of both system parameters and initial conditions. Time series of trajectories, Lyapunov exponents, and bifurcations of the hidden chaotic attractor are reported. Basins of attraction of individual equilibria are depicted to verify that the hidden chaotic attractor is found. Dynamic regions of attractors are illustrated to reveal seamless connections between self-excited and hidden chaotic attractors in the classical Lorenz system with wide ranges of parameters.

Keywords: Nonlinear system; Chaos; Lorenz system; Self-excited attractor; Hidden attractor (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (11)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077917305192
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:107:y:2018:i:c:p:61-66

DOI: 10.1016/j.chaos.2017.12.017

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. ().