Hopf bifurcation in the evolution of networks driven by spike-timing-dependent plasticity

Quansheng Ren, Kiran M. Kolwankar, Areejit Samal, and Jürgen Jost
Phys. Rev. E 86, 056103 – Published 6 November 2012

Abstract

We study the interplay of topology and dynamics in a neural network connected with spike-timing-dependent plasticity (STDP) synapses. Stimulated with periodic spike trains, the STDP-driven network undergoes a synaptic pruning process and evolves to a residual network. We examine the variation of topological and dynamical properties of the residual network by varying two key parameters of STDP: synaptic delay and the ratio between potentiation and depression. Our extensive numerical simulations of the leaky integrate-and-fire model show that there exists two regions in the parameter space. The first corresponds to fixed-point configurations, where the distribution of peak synaptic conductances and the firing rate of neurons remain constant over time. The second corresponds to oscillating configurations, where both topological and dynamical properties vary periodically, which is a result of a fixed point becoming a limit cycle via a Hopf bifurcation. This leads to interesting questions regarding the implications of these rhythms in the topology and dynamics of the network for learning and cognitive processing.

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  • Received 24 April 2012

DOI:https://doi.org/10.1103/PhysRevE.86.056103

©2012 American Physical Society

Authors & Affiliations

Quansheng Ren1,2,*, Kiran M. Kolwankar2,3,†, Areejit Samal2,4,‡, and Jürgen Jost2,5,§

  • 1School of Electronics Engineering and Computer Science, Peking University, Beijing 100871, China
  • 2Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, D-04103 Leipzig, Germany
  • 3Department of Physics, Ramniranjan Jhunjhunwala College, Ghatkopar (W), Mumbai 400 086, India
  • 4Laboratoire de Physique Théorique et Modèles Statistiques, CNRS and Univ Paris-Sud, UMR 8626, F-91405 Orsay, France
  • 5The Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA

  • *qsren@pku.edu.cn
  • kiran.kolwankar@gmail.com
  • samal@mis.mpg.de
  • §jost@mis.mpg.de

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Issue

Vol. 86, Iss. 5 — November 2012

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