Strange waves in the ensemble of van der pol oscillators

A. V. Shabunin

Izvestiya VUZ. Applied Nonlinear Dynamics, Tome 28 (2020) no. 2, pp. 186-200.

Résumé

The purpose of this paper is to study the processes of spatial disorder and the development of phase multistability in a discrete medium of anharmonic oscillators. Methods. An ensemble of diffusively coupled van der Pol oscillators is used as a model of discrete anharmonic medium. The model is investigated by numerical simulation; its phase dynamics is studied. The formed spatial structures are visualized by means of phase difference distribution. Results. It is shown that the ensemble of van der Pol generators demonstrates spatially irregular wave modes when the parameter of anharmonicity exceeds certain threshold value. This phenomenon is similar to appearance of strange waves in ensemble of anharmonic phase oscillators. Regularities of evolution of these waves with parameters change are investigated. Regions of existence and stability of the waves are built. It is shown that the strange wave modes form multistability, since stability regions of waves with different numbers of phase defects overlap. Conclusion. Transition from harmonic to relaxation oscillations can be followed by a spatial disorder, because of phase failures that might take place at arbitrary points of the discrete self-oscillating medium. This effect increases with the growth of anharmonicity. As a result, the medium is divided into a lot of clusters with almost in-phase and out-of-phase behaviors. Such clusters interact, demonstrating mutual repulsion. The observed phenomena may be interesting for understanding the processes of spatial organization and formation of structures in self-oscillating media with simple temporal dynamics.

Détail

Keywords: oscillations and waves, multistability, spatial structures.