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  • 1Department of Mathematics, National Institute of Technology, Durgapur 713209, India.

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Summary
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We developed a new adaptive coupling strategy to achieve explosive synchronization in complex networks. This method enhances synchronization width and reduces the impact of phase frustration, ensuring robust network behavior.

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Area of Science:

  • Complex Networks
  • Nonlinear Dynamics
  • Statistical Physics

Background:

  • Phase oscillators in complex networks often exhibit synchronization phenomena.
  • Controlling synchronization, particularly explosive synchronization and hysteresis, is crucial for understanding network dynamics.
  • Phase frustration can disrupt synchronized states in networks.

Purpose of the Study:

  • To introduce an adaptive coupling strategy for inducing and enhancing hysteresis/explosive synchronization in phase oscillator networks.
  • To investigate the strategy's ability to manage phase frustration and ensure robust synchronization.
  • To develop a theoretical framework for predicting synchronization transitions.

Main Methods:

  • Implementation of an adaptive coupling strategy within the Sakaguchi-Kuramoto model.
  • Design of specific oscillator frequency sets to promote in-phase synchronization.
  • Application of mean-field analysis to derive a semi-analytical formalism.

Main Results:

  • The adaptive coupling strategy successfully induces explosive synchronization with significantly enhanced width.
  • The strategy effectively diminishes the impact of phase frustration by creating an enhanced hysteresis loop.
  • A semi-analytical formalism accurately predicts the backward transition of the synchronization order parameter.

Conclusions:

  • The proposed adaptive coupling strategy offers a robust method for controlling explosive synchronization in complex networks.
  • This approach mitigates negative effects of phase frustration, demonstrating broad applicability across network structures and frequency distributions.
  • The developed formalism provides a valuable tool for analyzing and predicting synchronization dynamics in such systems.