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Cooperative behavior between oscillatory and excitable units: the peculiar role of positive coupling-frequency correlations

  • Bernard Sonnenschein
  • Thomas K. DM. Peron
  • Francisco A. Rodrigues
  • Jürgen Kurths
  • Lutz Schimansky-Geier
Open Access
Regular Article

Abstract

We study the collective dynamics of noise-driven excitable elements, so-called active rotators. Crucially here, the natural frequencies and the individual coupling strengths are drawn from some joint probability distribution. Combining a mean-field treatment with a Gaussian approximation allows us to find examples where the infinite-dimensional system is reduced to a few ordinary differential equations. Our focus lies in the cooperative behavior in a population consisting of two parts, where one is composed of excitable elements, while the other one contains only self-oscillatory units. Surprisingly, excitable behavior in the whole system sets in only if the excitable elements have a smaller coupling strength than the self-oscillating units. In this way positive local correlations between natural frequencies and couplings shape the global behavior of mixed populations of excitable and oscillatory elements.

Keywords

Statistical and Nonlinear Physics 

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Copyright information

© The Author(s) 2014

Authors and Affiliations

  • Bernard Sonnenschein
    • 1
    • 2
  • Thomas K. DM. Peron
    • 3
  • Francisco A. Rodrigues
    • 4
  • Jürgen Kurths
    • 1
    • 2
  • Lutz Schimansky-Geier
    • 1
    • 2
  1. 1.Department of PhysicsHumboldt-Universität zu BerlinBerlinGermany
  2. 2.Bernstein Center for Computational Neuroscience Berlin, Philippstrasse 13BerlinGermany
  3. 3.Instituto de Física de São Carlos, Universidade de São PauloSão CarlosBrazil
  4. 4.Departamento de Matemática Aplicada e Estatística, Instituto de Ciências Matemáticas e de Computação, Universidade de São PauloSão CarlosBrazil

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