Synchronization Patterns and Waves

• Applicant: Professor Dr. Arkady Pikovsky
• Subject Area: Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics
• Term: from 2019 to 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 409273578

• Final Report Year: 2023

Final Report Abstract

Synchronization is a fundamental phenomenon for coupled oscillators: they can adjust their phases and frequencies depending on the properties of the coupling. Considering oscillators spread in space, synchrony can be observed in some parts, while other parts remain asynchronous. These structures can stay, forming synchronous patterns on top of asynchronous environment (often called chimera patterns), or they can move, forming synchronization waves. In this project, we have studied different arrangements that lead to synchronization patterns and waves. One line of research deals with the motility of the underlying oscillators. We show, quite unexpectedly, that random motility (e.g., when oscillators diffuse) favors the formation of chimera states. In another case, when the coupling medium moves as a whole, the effective interaction between oscillators becomes asymmetric in space. This leads to moving chimera-like states, the properties of which we studied in detail. Another line of research was related to the effects of disorder. We studied how disorder in a one-dimensional array of oscillators prevents the establishment of synchrony; in another work we described possible synchronization patterns in an array of oscillators with distributed natural frequencies. Our other surprising finding is that a solitary chimera pattern (chimera soliton) starts to move due to an effective randomness due to a finite density of oscillators. Rather counterintuitively, this motion is highly ordered and not a random walk as reported for other chimera patterns.

Publications

• Disorder fosters chimera in an array of motile particles. Physical Review E, 104(3).
  Smirnov, L. A.; Bolotov, M. I.; Osipov, G. V. & Pikovsky, A.
  
• Spatiotemporal Regimes in the Kuramoto–Battogtokh System of Nonidentical Oscillators. Journal of Experimental and Theoretical Physics, 132(1), 127-147.
  Bolotov, M. I.; Smirnov, L. A.; Bubnova, E. S.; Osipov, G. V. & Pikovsky, A. S.
  
• Finite-density-induced motility and turbulence of chimera solitons. New Journal of Physics, 24(4), 043042.
  Smirnov, L. A.; Bolotov, M. I.; Bolotov, D. I.; Osipov, G. V. & Pikovsky, A.
  
• Phase-locking dynamics of heterogeneous oscillator arrays. Chaos, Solitons & Fractals, 155, 111721.
  Lepri, Stefano & Pikovsky, Arkady