Séminaire Yuri Maistrenko

Jeudi 09 Octobre 2014 (14h00, salle G001)

Yuri Maistrenko, Académie des sciences de Kiev (Ukraine), Université technique de Darmstadt (Allemagne).

Titre : Cascades of multi-headed chimera states.

Résumé : Chimera state is a remarkable space-temporal pattern in nonlocally coupled dynamical systems, that displays a self-organized behavior of co-existing coherence and incoherence.

It was found in 2002 by Kuramoto and Battogtock [1] as a spontaneous symmetry breaking for complex Ginzburg-Landau equation and its phase approximation known as Kuramoto model. Currently, this is an area of intense theoretical and experimental research, for now, chimeras have been found in many systems from various fields. In this talk, I report cascades of chimera states which are characterized by increasing number of intervals of irregularity (chaoticity), so-called chimera's heads. Parameter regions for the multi-headed chimera states are obtained. The regions are heavily intersecting such that chimeras of different head’s numbers can co-exist [2]. In two-dimensions, chimera states are found in the form of incoherent/coherent spots or strips as well as spirals with incoherent core [3]. In thee-dimensions they are incoherent/coherent balls and layers, also scroll waves with swelled incoherent filaments of various space configuration and modularity [4]. The presentation is illustrated by 3D videos of the complex chimera dynamics.

[1] Y. Kuramoto & D. Battogtokh. [2002] ”Coexistence of coherence and incoherence in nonlocally coupled phase oscillators”, Nonlinear Phenom. Complex Syst. 5, 380–385.

[2] Yu. Maistrenko, A. Vasylenko, O. Sudakov, R. Levchenko & V. Maistrenko. [2014] ”Cascades of multi-headed chimera states for coupled phase oscillators”, Int. J. Bif. &Chaos. 24, 1440014.

[3] O. Omel’chenko, M. Wolfrum, S. Yanchuk, Yu. Maistrenko & O. Sudakov. [2012] ”Stationary patterns of coherence and incoherence in two-dimensional arrays of non-locally-coupled phase oscillators”, Phys. Rev. E. 85, 036210. [4] V.Maistrenko, O.Sudakov, O.Osiv, and Yu.Maistrenko. [2014] “Chimeras living in three-dimensions” (in preparation) .