PMID: 11308735Apr 20, 2001Paper

Transcritical riddling in a system of coupled maps

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Oleksandr V PopovychJ Kurths

Abstract

The transition from fully synchronized behavior to two-cluster dynamics is investigated for a system of N globally coupled chaotic oscillators by means of a model of two coupled logistic maps. An uneven distribution of oscillators between the two clusters causes an asymmetry to arise in the coupling of the model system. While the transverse period-doubling bifurcation remains essentially unaffected by this asymmetry, the transverse pitchfork bifurcation is turned into a saddle-node bifurcation followed by a transcritical riddling bifurcation in which a periodic orbit embedded in the synchronized chaotic state loses its transverse stability. We show that the transcritical riddling transition is always hard. For this, we study the sequence of bifurcations that the asynchronous point cycles produced in the saddle-node bifurcation undergo, and show how the manifolds of these cycles control the magnitude of asynchronous bursts. In the case where the system involves two subpopulations of oscillators with a small mismatch of the parameters, the transcritical riddling will be replaced by two subsequent saddle-node bifurcations, or the saddle cycle involved in the transverse destabilization of the synchronized chaotic state may smoothly...Continue Reading

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Citations

Oct 14, 2016·SpringerPlus·Behnaz Koocheck ShooshtariMohammadReza Molaei
Feb 28, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Alexey Jalnine, Sang-Yoon Kim
Apr 3, 2013·Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences·Fengrong ZhangJürgen Kurths
Feb 9, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·G TanakaK Aihara
Mar 15, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Sang-Yoon KimSergey P Kuznetsov
Feb 3, 2004·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Sang-Yoon KimBrian Hunt
Jul 20, 2001·Physical Review Letters·A PikovskyY Maistrenko

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