Cooperative behavior between oscillatory and excitable units: the peculiar role of positive coupling-frequency correlations
1 Department of Physics, Humboldt-Universität zu Berlin, Newtonstrasse 15, 12489 Berlin, Germany
2 Bernstein Center for Computational Neuroscience Berlin, Philippstrasse 13, 10115 Berlin, Germany
3 Instituto de Física de São Carlos, Universidade de São Paulo, Avenida Trabalhador São Carlense 400, Caixa Postal 668, CEP 13560-970 São Carlos, São Paulo, Brazil
4 Departamento de Matemática Aplicada e Estatística, Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, Caixa Postal 668, 13560-970 São Carlos, São Paulo, Brazil
Received: 28 April 2014
Received in final form: 18 June 2014
Published online: 11 August 2014
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.
Key words: Statistical and Nonlinear Physics
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