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Amplitude death with mean-field diffusion.

Amit Sharma1, Manish Dev Shrimali

  • 1The LNM Institute of Information Technology, Jaipur, India.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 26, 2012
PubMed
Summary
This summary is machine-generated.

Mean-field diffusive coupling in nonlinear oscillators causes amplitude death through synchronization. A general criterion for this phenomenon was derived and verified across multiple systems.

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Area of Science:

  • Nonlinear dynamics
  • Complex systems
  • Network science

Background:

  • Nonlinear oscillators exhibit complex behaviors.
  • Coupling mechanisms significantly influence system dynamics.
  • Amplitude death is a phenomenon where oscillations cease.

Purpose of the Study:

  • To investigate amplitude death in nonlinear oscillators with mean-field diffusive coupling.
  • To establish a general criterion for amplitude death in such systems.
  • To analyze the synchronization transition leading to amplitude death.

Main Methods:

  • Numerical simulations of coupled nonlinear oscillators.
  • Analysis of parameter space for coupling strength and mean-field control.
  • Characterization using average phase difference, Lyapunov exponents, and average amplitude.

Main Results:

  • Identified amplitude death as a result of synchronization transition.
  • Derived a general criterion for amplitude death under mean-field diffusion.
  • Observed this behavior in Landau-Stuart, Rössler, Lorenz, FitzHugh-Nagumo, and Chua systems.

Conclusions:

  • Mean-field diffusive coupling effectively induces amplitude death.
  • The derived criterion provides a universal understanding of this transition.
  • The findings are applicable to diverse nonlinear dynamical systems.