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arXiv · 1507.01918

Stable and transient multi-cluster oscillation death in nonlocally coupled networks

Isabelle Schneider·Marie Kapeller·Sarah Loos·Anna Zakharova·Bernold Fiedler·Eckehard Schöll
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Abstract

In a network of nonlocally coupled Stuart-Landau oscillators with symmetry-breaking coupling, we study numerically, and explain analytically, a family of inhomogeneous steady states (oscillation death). They exhibit multi-cluster patterns, depending on the cluster distribution prescribed by the initial conditions. Besides stable oscillation death, we also find a regime of long transients asymptotically approaching synchronized oscillations. To explain these phenomena analytically in dependence on the coupling range and the coupling strength, we first use a mean-field approximation which works well for large coupling ranges but fails for coupling ranges which are small compared to the cluster size. Going beyond standard mean-field theory, we predict the boundaries of the different stability regimes as well as the transient times analytically in excellent agreement with numerical results.

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Isabelle Schneider, Marie Kapeller, Sarah Loos, Anna Zakharova, Bernold Fiedler, Eckehard Schöll. 2015-10-12. Stable and transient multi-cluster oscillation death in nonlocally coupled networks. https://doi.org/10.1103/physreve.92.052915

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