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Updated: Jun 23, 2026
06:42
Magnetically Induced Rotating Rayleigh-Taylor Instability
Published on: March 3, 2017
Diffusion-induced instability and chaos in random oscillator networks.
Hiroya Nakao1, Alexander S Mikhailov
1Department of Physics, Kyoto University, Kyoto 606-8502, Japan.
Summary
Diffusively coupled oscillators on random networks show complex dynamics like partial amplitude death and chaos. This instability, analogous to the Benjamin-Feir instability, arises from spontaneous phase modulations in uniform oscillations.
Area of Science:
- Complex systems
- Nonlinear dynamics
- Network science
Background:
- Limit-cycle oscillators are fundamental in describing periodic phenomena.
- Diffusional coupling can introduce complex behaviors in coupled oscillator systems.
- Random networks provide a framework for studying emergent dynamics.
Purpose of the Study:
- To investigate complex dynamical patterns in diffusively coupled limit-cycle oscillators on random networks.
- To analyze the role of spontaneous phase modulations and their connection to the Benjamin-Feir instability.
- To develop a theoretical framework for understanding the observed nonlinear dynamics.
Main Methods:
- Modeling the system as a network analog of the complex Ginzburg-Landau equation.
- Analyzing the linear stability of uniform oscillations with respect to phase modulations.
- Conducting numerical simulations on random scale-free networks.
- Constructing a dynamic mean-field theory.
Main Results:
- Demonstrated various complex dynamical patterns, including partial amplitude death, clustering, and chaos.
- Identified uniform oscillations as linearly unstable due to diffusional coupling, analogous to the Benjamin-Feir instability.
- Revealed a wealth of complex regimes in random scale-free networks.
Conclusions:
- Diffusional coupling in random oscillator networks can lead to rich and complex nonlinear dynamics.
- The Benjamin-Feir instability plays a crucial role in destabilizing uniform oscillations.
- The developed dynamic mean-field theory effectively explains the observed nonlinear phenomena.
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