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Dynamical effects of integrative time-delay coupling.

Garima Saxena1, Awadhesh Prasad, Ramakrishna Ramaswamy

  • 1Department of Physics and Astrophysics, University of Delhi, Delhi, India. gsaxena2006@yahoo.co.in

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 28, 2010
PubMed
Summary
This summary is machine-generated.

Integrative coupling in dynamical systems, where signals accumulate over time τ, broadens the range of amplitude death. A critical coupling strength causes a discontinuous frequency change in oscillations.

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Area of Science:

  • Complex Systems
  • Nonlinear Dynamics
  • Theoretical Physics

Background:

  • Coupled dynamical systems are fundamental to understanding complex phenomena.
  • Integrative coupling, where influence accumulates over time τ, presents unique behaviors.
  • Amplitude death, the cessation of oscillations, is a key phenomenon in coupled systems.

Purpose of the Study:

  • To investigate the impact of integrative coupling on dynamical systems.
  • To analyze the occurrence and parameter space of amplitude death under integrative coupling.
  • To explore the relationship between coupling strength, time interval τ, and oscillatory behavior.

Main Methods:

  • Analytical estimation for the Landau-Stuart model (limit cycle oscillators).
  • Numerical simulations for coupled chaotic Lorenz oscillators.
  • Analysis of coupling signals integrated over a time interval τ.

Main Results:

  • Integrative coupling leads to amplitude death over a wider parameter range and in a single region.
  • An analytic estimate for the amplitude death region boundary was derived for limit cycle oscillators.
  • Numerical results for chaotic oscillators demonstrate similar behavior.
  • A critical coupling strength was identified, causing a discontinuous frequency change.

Conclusions:

  • Integrative coupling significantly alters the dynamics of coupled systems, particularly concerning amplitude death.
  • The findings provide a theoretical and numerical understanding of amplitude death in systems with cumulative coupling.
  • Discontinuous frequency changes at critical coupling strengths highlight the complex response of these systems to integrative interactions.