Chimera regimes in a ring of elements with local unidirectional interaction

I. A. Shepelev ; T. E. Vadivasova

Russian journal of nonlinear dynamics, Tome 12 (2016) no. 2, pp. 197-209.

Résumé

Complex spatial structures, called chimeras, are the subject of considerable recent interest. They consist of stationary areas with coherent and incoherent behavior of neighboring elements. A number of problems related to similar structures have not been solved yet. One of these problems concerns the element interaction in ensembles, when stable chimera structures can be observed. Until quite recently it was assumed that one of the most important conditions for the existence of chimeras is the nonlocal character of interaction. However, this assumption is not exactly correct. Chimeras can be realized for special types of local coupling. So, the chimera examples were obtained in ensembles with inertial local coupling. The additional variable is introduced for a coupling specification. It is given by a linear differential equation. Also, the so-called virtual chimeras exist in oscillators with delayed feedback. This allows one to assume that chimera states can be obtained in a ring of local coupling oscillators with unidirectional interaction, which is inertialess, but has a nonlinear character. This assumption is based on a qualitative similarity between the behaviors of an oscillator with delay feedback and a ring of the same oscillators with local unidirectional coupling. The basis of this work is the system with delay feedback, which demonstrates the existence of a virtual chimera. The distributed analog is investigated. It is an oscillator ring with unidirectional nonlinear local coupling. The existence of chimera structures in the ring were found in the special area of parameter changing via computing simulation. This chimera moves in a ring with constant velocity and is similar to the chimera in the system with delay feedback. The area of chimera existence of parameter variations was studied. Regime diagrams were plotted on the plane of control parameters. The scenario of chimera destruction for the coupling increase was shown.

Détail

Keywords: oscillator with delayed feedback, distributed system, dynamical chaos, local coupling.
Mots-clés : spatial structure, chimera

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