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Three-body interactions with time delay.

Rajat Karnatak1

  • 1Theoretical Physics/Complex Systems, ICBM, Carl von Ossietzky University of Oldenburg, Carl-von-Ossietzky-Straße 9-11, Box 2503, 26111 Oldenburg, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 16, 2013
PubMed
Summary

This study analyzes globally coupled phase oscillators with three-body interactions and time delays, providing stability estimates and synchronization frequencies for these complex dynamics.

Area of Science:

  • Complex systems
  • Nonlinear dynamics
  • Theoretical physics

Background:

  • Globally coupled phase oscillators are fundamental models in understanding synchronization phenomena.
  • Investigating multi-body interactions and time delays is crucial for realistic system modeling.

Purpose of the Study:

  • To analyze the stability of incoherent solutions in globally coupled phase oscillators with three-body interactions and time delay.
  • To derive and validate theoretical expressions for phase synchronization frequencies and their stability.
  • To explore fluctuations in the synchronization order parameter and compare different coupling configurations.

Main Methods:

  • Analytical derivation of stability conditions for incoherent solutions.
  • Formulation of expressions for phase synchronization frequencies and their stability analysis.

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  • Numerical simulations to verify theoretical predictions and analyze synchronization order parameter fluctuations.
  • Comparative analysis of two-body, three-body, and mixed-coupled systems.

    • Main Results:

    • Analytic estimates for the stability of the incoherent solution were successfully derived.
    • Expressions for phase synchronization frequencies and their stability were obtained and validated numerically.
    • Numerical results revealed fluctuations in the synchronization order parameter.
    • Comparative studies highlighted differences in phase synchronization across various coupling schemes.

    Conclusions:

    • The study provides a robust theoretical and numerical framework for understanding the dynamics of complex oscillator systems.
    • Three-body interactions and time delays significantly influence phase synchronization stability and frequencies.
    • Further research can extend these findings to more intricate network topologies and interaction types.