Existence and stability of travelling wave states in a ring of non-locally coupled phase oscillators with propagation delays

Gautam C. Sethia; Abhijit Sen

doi:10.1103/physreve.84.066203

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arXiv · 1107.2991

Existence and stability of travelling wave states in a ring of non-locally coupled phase oscillators with propagation delays

Gautam C. Sethia·Abhijit Sen

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Abstract

We investigate the existence and stability of travelling wave solutions in a continuum field of non-locally coupled identical phase oscillators with distance-dependent propagation delays. A comprehensive stability diagram in the parametric space of the system is presented that shows a rich structure of multi-stable regions and illuminates the relative influences of time delay, the non-locality parameter and the intrinsic oscillator frequency on the dynamics of these states. A decrease in the intrinsic oscillator frequency leads to a break-up of the stability domains of the traveling waves into disconnected regions in the parametric space. These regions exhibit a tongue structure for high connectivity whereas they submerge into the stable region of the synchronous state for low connectivity. A novel finding is the existence of forbidden regions in the parametric space where no phase-locked solutions are possible. We also discover a new class of non-stationary \textit{breather} states for this model system that are characterized by periodic oscillations of the complex order parameter.

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Gautam C. Sethia, Abhijit Sen. 2011-12-12. Existence and stability of travelling wave states in a ring of non-locally coupled phase oscillators with propagation delays. https://doi.org/10.1103/physreve.84.066203

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