Séminaire de Mécanique d'Orsay

Le Vendredi 20 juin à 14h00 - Salle de conférences du LIMSI

Chimera state: a new scenario for laminar-turbulent coexistence?

Yuri Maistrenko
Professeur invité au FEMTO, Besançon, Univ. Franche-Comté *** Laboratory of Mathematical Modeling in Nonlinear Processes, Univ. Kiev, Nat. Acad. Sci. Ukraine

Chimera states represent remarkable patterns of spatially separated domains of coherence and incoherence. Intriguingly, this fascinating behavior can robustly develop in homogeneous media and oscillatory networks despite symmetric coupling and absence of external excitation. Chimera states emerge in wide regions of system parameters close to the transition between full coherence and incoherence, in many cases they co-exist with coherent or rotating flows.
Chimera states were discovered twelve years ago for complex Ginzburg-Landau equation and its phase approximation known as Kuramoto model [1]. Currently, this is an area of intense theoretical research. Recently, an experimental evidence of the chimera state has been proven for optical, chemical, mechanical, and optoelectronic systems.
I will give an overview of main features of the chimera state such as chaotic wandering, hyperchaotic Lyapunov spectrum, cascades of multi-headed chimeras with decreasing length scales etc. [2]. In two-dimensions, chimera states acquire the form of incoherent or coherent spots and strips, also spirals with incoherent core [3]. Finally, I will present the first observation of three-dimensional chimera states: streamwise vortexes with incoherent core, and incoherent ball surrounded by regular flow.
The purpose of this talk is to discuss with the audience, if chimera state can serve as a prototype of laminar-turbulent patterns in fluids? In particular, how could one relate the chimera model parameters, coupling range and interaction phase shift, with Reynolds number and other fluid dynamics quantities?
[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” (http://arxiv.org/pdf/1402.1363v2.pdf).
[3] O. Omel’chenko, M. Wolfrum, S. Yanchuk, Yu. Maistrenko & O. Sudakov. [2012] ”Stationary patterns of coherence and incoherence in twodimensional arrays of non-locally-coupled phase oscillators”, Phys. Rev. E. 85, 036210.