The Kuramoto model with distributed shear

Details The Kuramoto model with distributed shear The Kuramoto model with distributed shear

2011-09-22

arxiv.org/abs/1109.4783v1

EPL 95, 60007 (2011)

Nonlinear Sciences

Adaptation and Self-Organizing Systems

6 pages

Scientific paper

10.1209/0295-5075/95/60007

We uncover a solvable generalization of the Kuramoto model in which shears (or nonisochronicities) and natural frequencies are distributed and statistically dependent. We show that the strength and sign of this dependence greatly alter synchronization and yield qualitatively different phase diagrams. The Ott-Antonsen ansatz allows us to obtain analytical results for a specific family of joint distributions. We also derive, using linear stability analysis, general formulae for the stability border of incoherence.

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