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Schneider I, Kapeller M, Loos S, et al. Stable and transient multicluster oscillation death in nonlocally coupled networks. Phys Rev E Stat Nonlin Soft Matter Phys. 2015;92(5):052915doi: 10.1103/PhysRevE.92.052915.
Schneider, I., Kapeller, M., Loos, S., Zakharova, A., Fiedler, B., & Schöll, E. (2015). Stable and transient multicluster oscillation death in nonlocally coupled networks. Physical review. E, Statistical, nonlinear, and soft matter physics, 92(5), 052915. https://doi.org/10.1103/PhysRevE.92.052915
Schneider, Isabelle, et al. "Stable and transient multicluster oscillation death in nonlocally coupled networks." Physical review. E, Statistical, nonlinear, and soft matter physics vol. 92,5 (2015): 052915. doi: https://doi.org/10.1103/PhysRevE.92.052915
Schneider I, Kapeller M, Loos S, Zakharova A, Fiedler B, Schöll E. Stable and transient multicluster oscillation death in nonlocally coupled networks. Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Nov;92(5):052915. doi: 10.1103/PhysRevE.92.052915. Epub 2015 Nov 30. PMID: 26651770.
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Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Nov;92(5):052915. doi: 10.1103/PhysRevE.92.052915. Epub 2015 Nov 30.

Stable and transient multicluster oscillation death in nonlocally coupled networks.

Physical review. E, Statistical, nonlinear, and soft matter physics

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

Affiliations

  1. Institut für Mathematik, Freie Universität Berlin, Arnimallee 7, 14195 Berlin, Germany.
  2. Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany.

PMID: 26651770 DOI: 10.1103/PhysRevE.92.052915

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 multicluster 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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