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Route to synchronization in coupled phase oscillators with frequency-dependent coupling: Explosive or continuous?

Mohit Kumar*

Sayan Gupta†

  • Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai 600036, India

  • Department of Applied Mechanics, Indian Institute of Technology Madras, Chennai 600036, India and Complex Systems and Dynamics Group, Indian Institute of Technology Madras, Chennai, 600036, India

  • *mohitkumar.2k1@gmail.com
  • †sayan@iitm.ac.in
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Phys. Rev. E 106, 044310 – Published 31 October, 2022

DOI: https://doi.org/10.1103/PhysRevE.106.044310

Abstract

Interconnected dynamical systems often transition between states of incoherence and synchronization due to changes in system parameters. These transitions could be continuous (gradual) or explosive (sudden) and may result in failures, which makes determining their nature important. In this study, we abstract dynamical networks as an ensemble of globally coupled Kuramoto-like phase oscillators with frequency-dependent coupling and investigate the mechanisms for transition between incoherent and synchronized dynamics. The characteristics that dictate a continuous or explosive route to synchronization are the distribution of the natural frequencies of the oscillators, quantified by a probability density function g(ω), and the relation between the coupling strength and natural frequency of an oscillator, defined by a frequency-coupling strength correlation function f(ω). Our main results are conditions on f(ω) and g(ω) that result in continuous or explosive routes to synchronization and explain the underlying physics. The analytical developments are validated through numerical examples.

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Phys. Rev. E 106, 044310– Published 31 October, 2022
  • Received 28 July 2022
  • Accepted 11 October 2022
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