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General mechanism for amplitude death in coupled systems
V Resmi1, G Ambika, R E Amritkar
1Indian Institute of Science Education and Research, Pune 411021, India. v.resmi@iiserpune.ac.in
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 21, 2011
Summary
We discovered a new mechanism causing amplitude death in coupled dynamical systems. Indirect feedback coupling competes with direct coupling, leading to synchronization or antisynchronization and eventual amplitude death.
Area of Science:
- Physics
- Nonlinear Dynamics
- Complex Systems
Background:
- Coupled dynamical systems can synchronize via direct coupling.
- Indirect feedback coupling can induce antisynchronization.
- Amplitude death is a phenomenon where coupled oscillators cease coherent behavior.
Purpose of the Study:
- To introduce a general mechanism for amplitude death in coupled synchronizable dynamical systems.
- To analyze the stability and transition types for amplitude death.
- To demonstrate the generality of the mechanism across various system dynamics and coupling types.
Main Methods:
- General stability analysis to determine thresholds for amplitude death.
- Investigation of transition dynamics (continuous and discontinuous).
- Application to diverse systems: periodic, chaotic, hyperchaotic, and time-delay systems.
Main Results:
- A general mechanism for amplitude death is identified, arising from competing direct and indirect coupling effects.
- Threshold values for the onset of amplitude death are derived.
- Transitions to amplitude death can be continuous or discontinuous.
- The mechanism is shown to be robust across various system dynamics and coupling types.
Conclusions:
- The proposed mechanism provides a unified framework for understanding amplitude death in a wide range of coupled dynamical systems.
- The findings offer insights into controlling or inducing cessation of oscillations in complex systems.
- This work highlights the crucial role of indirect feedback in modulating collective dynamics.
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