Desynchronization in diluted neural networks

Rüdiger Zillmer, Roberto Livi, Antonio Politi, and Alessandro Torcini
Phys. Rev. E 74, 036203 – Published 5 September 2006

Abstract

The dynamical behavior of a weakly diluted fully inhibitory network of pulse-coupled spiking neurons is investigated. Upon increasing the coupling strength, a transition from regular to stochasticlike regime is observed. In the weak-coupling phase, a periodic dynamics is rapidly approached, with all neurons firing with the same rate and mutually phase locked. The strong-coupling phase is characterized by an irregular pattern, even though the maximum Lyapunov exponent is negative. The paradox is solved by drawing an analogy with the phenomenon of “stable chaos,” i.e., by observing that the stochasticlike behavior is “limited” to an exponentially long (with the system size) transient. Remarkably, the transient dynamics turns out to be stationary.

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  • Received 7 March 2006

DOI:https://doi.org/10.1103/PhysRevE.74.036203

©2006 American Physical Society

Authors & Affiliations

Rüdiger Zillmer1,*, Roberto Livi2,3,†, Antonio Politi4,5,‡, and Alessandro Torcini4,5,§

  • 1INFN Sezione Firenze, via Sansone 1, I-50019 Sesto Fiorentino, Italy
  • 2Dipartimento di Fisica, Universitá di Firenze, via Sansone 1, I-50019 Sesto Fiorentino, Italy
  • 3Sezione INFN, Unita’ INFM e Centro Interdipartimentale per lo Studio delle Dinamiche Complesse, via Sansone 1, I-50019 Sesto Fiorentino, Italy
  • 4Istituto dei Sistemi Complessi, CNR, CNR, via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy
  • 5Centro Interdipartimentale per lo Studio delle Dinamiche Complesse, via Sansone 1, I-50019 Sesto Fiorentino, Italy

  • *Electronic address: zillmer@fi.infn.it
  • Electronic address: livi@fi.infn.it
  • Electronic address: antonio.politi@isc.cnr.it
  • §Electronic address: alessandro.torcini@isc.cnr.it

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Issue

Vol. 74, Iss. 3 — September 2006

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