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Adaptive oscillator networks with conserved overall coupling: Sequential firing and near-synchronized states

Clara B. Picallo1,2,* and Hermann Riecke3,4

  • 1Instituto de Física de Cantabria (IFCA), CSIC-UC, E-39005 Santander, Spain
  • 2Departamento de Física Moderna, Universidad de Cantabria, E-39005 Santander, Spain
  • 3Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, Illinois 60208, USA
  • 4Northwestern Institute on Complex Systems, Northwestern University, Evanston, Illinois 60208, USA

  • *current address: Department D'Estructura i constituents de la Materia.Universitat de Barcelona, E-08028 Barcelona, Spain
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Phys. Rev. E 83, 036206 – Published 18 March, 2011

DOI: https://doi.org/10.1103/PhysRevE.83.036206

Abstract

Motivated by recent observations in neuronal systems we investigate all-to-all networks of nonidentical oscillators with adaptive coupling. The adaptation models spike-timing-dependent plasticity in which the sum of the weights of all incoming links is conserved. We find multiple phase-locked states that fall into two classes: near-synchronized states and splay states. Among the near-synchronized states are states that oscillate with a frequency that depends only very weakly on the coupling strength and is essentially given by the frequency of one of the oscillators, which is, however, neither the fastest nor the slowest oscillator. In sufficiently large networks the adaptive coupling is found to develop effective network topologies dominated by one or two loops. This results in a multitude of stable splay states, which differ in their firing sequences. With increasing coupling strength their frequency increases linearly and the oscillators become less synchronized. The essential features of the two classes of states are captured analytically in perturbation analyses of the extended Kuramoto model used in the simulations.

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Phys. Rev. E 83, 036206– Published 18 March, 2011
  • Received 3 August 2010
Article part of CHORUS

©2011 American Physical Society

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