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Partial amplitude death in delay-coupled oscillators with complete multipartite graphs.

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This study analytically investigates partial amplitude death in delay-coupled oscillators. We found coupling strength controls quenched oscillators, while delay impacts stability, not existence, of this phenomenon.

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Area of Science:

  • Physics
  • Nonlinear Dynamics
  • Network Science

Background:

  • Partial amplitude death (PAD) involves coupled oscillators reaching equilibrium while others maintain phase differences.
  • PAD in delay-coupled systems is observed numerically but lacks theoretical analysis.

Purpose of the Study:

  • To analytically investigate partial amplitude death (PAD) in delay-coupled oscillators within complete multipartite graphs.
  • To derive the amplitude-phase relationship during PAD and identify phase-locked patterns.

Main Methods:

  • Analytical investigation of delay-coupled oscillators.
  • Analysis of systems with complete multipartite graph topologies.
  • Derivation of amplitude-phase relationships and stability conditions.

Main Results:

  • Various phase-locked patterns of PAD exist for a given network topology.
  • Coupling strength determines the number of quenched oscillators.
  • Connection delay affects PAD stability but not its existence.

Conclusions:

  • The study provides an analytical framework for understanding PAD in complex networks.
  • Local stability analysis of PAD can be simplified to a time-invariant linear system.
  • Findings offer insights into controlling and predicting oscillator behavior in coupled systems.