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Using coupling imperfection to control amplitude death.

Frank Thomas Ndjomatchoua1, Byliole S Djouda1, Carlos Lawrence Gninzanlong1

  • 1Department of Physics, Faculty of Science, University of Yaoundé 1, P.O. Box 812, Ngoa Ekelle, Yaoundé, Cameroon.

Physical Review. E
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PubMed
Summary
This summary is machine-generated.

Local defects in oscillator networks can prevent amplitude death (AD), a phenomenon where oscillations cease. Network size and impurity strength are key factors in restoring oscillations, offering novel control mechanisms.

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Area of Science:

  • Complex Systems
  • Nonlinear Dynamics
  • Network Science

Background:

  • Amplitude death (AD) is a common phenomenon in nonlinear oscillator networks, typically induced by parameter tuning.
  • Previous research focused on homogeneous coupling, limiting understanding of oscillation control in imperfect systems.

Purpose of the Study:

  • To investigate the role of local defects in network connectivity on amplitude death.
  • To identify conditions where network imperfections can suppress AD and restore oscillations.

Main Methods:

  • Analysis of nonlinear oscillator networks with local defects in connectivity.
  • Theoretical analysis involving Hopf's bifurcation.
  • Numerical simulations across various mean-field coupled networks.

Main Results:

  • Local network defects can suppress amplitude death where homogeneous coupling fails.
  • A critical impurity strength, dependent on network size and system parameters, restores oscillations.
  • Network size significantly reduces the critical impurity strength required for oscillation restoration.

Conclusions:

  • Local inhomogeneities, often unavoidable, can serve as a mechanism for controlling oscillations in complex networks.
  • The findings offer a new perspective on oscillation dynamics, moving beyond idealized homogeneous systems.
  • Hopf's bifurcation plays a key role in destabilizing steady states and enabling oscillation restoration.