A unique chaotic snap system with a smoothly adjustable symmetry and nonlinearity: Chaos, offset-boosting, antimonotonicity, and coexisting multiple attractors

Gervais Dolvis Leutcho and Jacques Kengne

Chaos, Solitons & Fractals, 2018, vol. 113, issue C, 275-293

Abstract: This work proposes and systematically investigates the dynamics of a novel snap system with a single parameterized nonlinearity in the form φk(z)=0.5(exp(kz)−exp(−z)). The form of nonlinearity is physically interesting in the sense that the corresponding circuit realization involves only off-the shelf electronic components such as resistors, semiconductor diodes and operational amplifiers. Parameter k (i.e. a control resistor) serves to smoothly adjust the nonlinearity, and hence the symmetry of the system. In particular, for k=1, the nonlinearity is a hyperbolic sine, and thus the system is point symmetry about the origin. For k ≠ 1, the system is non-symmetric. The fundamental dynamics of the system are investigated in terms of equilibria and stability, phase space trajectory plots, bifurcations diagrams, and graphs of Lyapunov exponents. When monitoring the system parameters, some striking phenomena are found including period doubling bifurcation, reverse bifurcations, merging crises, coexisting bifurcations, hysteresis and offset boosting. Several windows in the parameters space are depicted in which the novel snap system displays a plethora of coexisting attractors (i.e. two, three, four, five or six different attractors) depending solely on the choice of the initial conditions. The magnetization of the state space due to the presence of multiple competing solutions is illustrated by means of basins of attraction. Laboratory experimental results confirm the theoretical predictions.

Keywords: Unique chaotic snap system; Offset-boosting; Antimonotonicity; Coexisting attractors; Experimental study (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077918302728
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:113:y:2018:i:c:p:275-293

DOI: 10.1016/j.chaos.2018.05.017

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. ().