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Amplitude death in nonlinear oscillators with mixed time-delayed coupling.

Wei Zou1, D V Senthilkumar, Yang Tang

  • 1School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China and Institute of Physics, Humboldt University Berlin, Berlin D-12489, Germany and Potsdam Institute for Climate Impact Research, Telegraphenberg, Potsdam D-14415, Germany.

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Amplitude death (AD) occurs when coupled oscillators stop oscillating. This study shows mixed time-delayed coupling promotes AD more effectively than purely instantaneous or delayed coupling, enhancing our understanding of delay-induced phenomena.

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Area of Science:

  • Nonlinear dynamics
  • Complex systems
  • Coupled oscillators

Background:

  • Amplitude death (AD) is a phenomenon where coupled oscillating systems cease to oscillate.
  • Understanding the influence of coupling types on AD is crucial for controlling oscillatory behaviors.

Purpose of the Study:

  • Investigate amplitude death in nonlinear oscillators with mixed time-delayed coupling.
  • Determine how combinations of instantaneous and time-delayed coupling affect AD onset.

Main Methods:

  • Analysis of nonlinear oscillators with mixed coupling.
  • Exploration of parameter spaces for instantaneous and time-delayed coupling combinations.

Main Results:

  • Mixed time-delayed coupling broadens the parameter range for AD onset compared to purely instantaneous or delayed coupling.
  • Identical coupled oscillators exhibit AD with instantaneous coupling combined with a small fraction of time-delayed coupling.

Conclusions:

  • Mixed time-delayed coupling is a significant factor in inducing amplitude death.
  • This research provides novel insights into delay-induced amplitude death in coupled nonlinear systems.