Control of chaos in a three-well duffing system

Jianping Yang and Zhujun Jing

Chaos, Solitons & Fractals, 2009, vol. 41, issue 3, 1311-1328

Abstract: Analytical and numerical results concerning control of chaos in a three-well duffing system with two external excitations are given by using the Melnikov methods proposed by Chacón et al. [Chacón R. General results on chaos suppression for biharmonically driven dissipative systems. Phys Lett A 1999;257:293–300, Chacón R, Palmero F, Balibrea F. Taming chaos in a driven Josephson Junction. Int J Bifurc Chaos 2001;11(7):1897–909, Chacón R. Role of ultrasubharmonic resonances in taming chaos by weak harmonic perturbations. Europhys Lett 2001;54(2):148C153]. We theoretically give the parameter-space region and intervals of initial phase difference for primary and subharmonic resonance and the necessary condition for the superharmonic and supersubharmonic resonance, where homoclinic chaos or heteroclinic chaos can be suppressed. Numerical simulations show the consistency and difference with theoretical analysis and the chaotic behavior can be converted to periodic orbits by adjusting amplitude and phase-difference of inhibiting excitation. Moreover, we consider the influence of parametric frequency on maximum Lyapunov exponent (LE) for different phase-differences, and give the distribution of maximum Lyapunov exponents in parameter-plane, which indicates the regions of non-chaotic states (non-positive LE) and chaotic states (positive LE).

Date: 2009
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077908002543
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:41:y:2009:i:3:p:1311-1328

DOI: 10.1016/j.chaos.2008.05.018

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. ().