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

Author(s)

Sonnenschein, Bernard ^{[1, 2]} ; Peron, Thomas K. D. M. ^[3] ; Rodrigues, Francisco A. ^[4] ; Kurths, Juergen ^{[1, 2]} ; Schimansky-Geier, Lutz ^{[1, 2]}

Affiliation

^[1] Humboldt Univ, Dept Phys, D-12489 Berlin - Germany

^[2] Bernstein Ctr Computat Neurosci Berlin, D-10115 Berlin - Germany

^[3] Univ Sao Paulo, Inst Fis Sao Carlos, BR-13560970 Sao Paulo - Brazil

^[4] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Dept Matemat Aplicada & Estat, BR-13560970 Sao Paulo - Brazil

• Document type: Journal article
• Source: European Physical Journal B; v. 87, n. 8 AUG 11 2014.
• Web of Science Citations: 9

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. (AU)

• FAPESP's process: 12/22160-7 - Synchronization of Kuramoto Oscillators in Complex Networks
• Grantee: Thomas Kaue Dal Maso Peron
• Support Opportunities: Scholarships in Brazil - Doctorate
• FAPESP's process: 13/26416-9 - Modelling of dynamical processes in complex networks
• Grantee: Francisco Aparecido Rodrigues
• Support Opportunities: Regular Research Grants