Bifurcation analysis of a simple 3D oscillator and chaos synchronization of its coupled systems

Tetsushi Ueta and Akihisa Tamura

Chaos, Solitons & Fractals, 2012, vol. 45, issue 12, 1460-1468

Abstract: Tamaševičius et al. proposed a simple 3D chaotic oscillator for educational purpose. In fact the oscillator can be implemented very easily and it shows typical bifurcation scenario so that it is a suitable training object for introductory education for students. However, as far as we know, no concrete studies on bifurcations or applications on this oscillator have been investigated. In this paper, we make a thorough investigation on local bifurcations of periodic solutions in this oscillator by using a shooting method. Based on results of the analysis, we study chaos synchronization phenomena in diffusively coupled oscillators. Both bifurcation sets of periodic solutions and parameter regions of in-phase synchronized solutions are revealed. An experimental laboratory of chaos synchronization is also demonstrated.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:45:y:2012:i:12:p:1460-1468

DOI: 10.1016/j.chaos.2012.08.007

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