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Related Experiment Videos

Breaking synchrony by heterogeneity in complex networks.

Michael Denker1, Marc Timme, Markus Diesmann

  • 1Max-Planck-Institut für Strömungsforschung and Fakultät für Physik, Universität Göttingen, 37073 Göttingen, Germany.

Physical Review Letters
|March 5, 2004
PubMed
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Coupling heterogeneity in pulse-coupled oscillator networks creates precise firing patterns, replacing synchrony. These patterns persist until disorder exceeds interaction delay, leading to asynchronous states. This study predicts and designs these complex network dynamics.

Area of Science:

  • Complex systems
  • Nonlinear dynamics
  • Computational neuroscience

Background:

  • Homogeneous networks of pulse-coupled oscillators typically exhibit global synchrony.
  • Understanding emergent dynamics in complex, heterogeneous networks is crucial for various scientific fields.

Purpose of the Study:

  • To investigate the impact of coupling heterogeneity on the dynamics of pulse-coupled oscillator networks.
  • To demonstrate the emergence of precisely timed periodic firing patterns in lieu of global synchrony.
  • To establish methods for predicting and designing specific network firing patterns.

Main Methods:

  • Analysis of pulse-coupled oscillator networks with complex and heterogeneous connectivity.
  • Derivation of self-consistency equations to model network behavior.

Related Experiment Videos

  • Investigation of the transition from periodic firing patterns to asynchronous states with increasing disorder.

    • Main Results:

    • Coupling heterogeneity induces precisely timed periodic firing patterns, replacing global synchrony.
    • These patterns remain stable up to a critical disorder level related to interaction delay.
    • Beyond this critical point, networks transition to asynchronous, aperiodic states.
    • Self-consistency equations accurately predict pattern temporal structure based on network properties.

    Conclusions:

    • Heterogeneity is key to achieving complex, timed firing patterns in oscillator networks.
    • The derived theoretical framework allows for prediction of network dynamics.
    • Custom heterogeneous coupling architectures can be designed to generate desired firing patterns.