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Stabilizing oscillation death by multicomponent coupling with mismatched delays.

Wei Zou¹, D V Senthilkumar, Yang Tang

¹School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China. zouwei2010@mail.hust.edu.cn

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|October 4, 2012

Summary

Networked oscillators with mismatched delays exhibit oscillation death (OD) across a wider parameter range. This multicomponent coupling strategy stabilizes networks and can be applied to neuronal and engineering systems.

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Area of Science:

Physics
Network Science
Dynamical Systems

Background:

Oscillation death (OD) is a phenomenon where coupled oscillators cease to oscillate.
Understanding network dynamics is crucial for various scientific and engineering fields.
Coupling oscillators with delays is a common scenario in real-world systems.

Purpose of the Study:

To investigate the dynamics of symmetric oscillator networks coupled via multiple components with mismatched delays.
To determine the impact of mismatched delays on the occurrence and stability of oscillation death.
To explore the potential applications of this coupling strategy.

Main Methods:

Analysis of coupled oscillator network dynamics.
Mathematical modeling of multicomponent coupling with mismatched delays.
Investigation of parameter domains for oscillation death.

Main Results:

Networked oscillators experience oscillation death (OD) over a larger parameter domain with mismatched delays compared to single-delay coupling.
OD is linearly stable for arbitrary symmetric networks with biased mismatched delays, even for large delays.
Increasing mismatch in coupling delays decreases the minimal intrinsic frequency required to induce OD.
The stabilizing effect is also observed in networked chaotic oscillators.

Conclusions:

Multicomponent coupling with mismatched delays significantly enhances the domain of oscillation death in networked oscillators.
This strategy offers a robust method for stabilizing complex networks, including chaotic systems.
The findings have potential applications in controlling pathological neuronal activities and in engineering design.