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Random symmetry breaking and freezing in chaotic networks.
Summary
A network of coupled oscillators exhibits chaotic dynamics where individual oscillator amplitudes freeze randomly. This leads to broken global symmetry and numerous coexisting chaotic attractors, demonstrating complex emergent behavior in coupled systems.
Area of Science:
- Nonlinear Dynamics and Chaos Theory
- Complex Systems and Network Science
- Statistical Physics
Background:
- Driven damped oscillators in double-well potentials exhibit distinct chaotic or nonchaotic trajectories based on amplitude sign oscillation.
- Coupled oscillator networks are fundamental to understanding emergent phenomena in complex systems.
Purpose of the Study:
- To investigate the dynamics of delay-coupled damped oscillators in a network.
- To explore the emergence of chaotic dynamics and symmetry breaking in such networks.
Main Methods:
- Analysis of the parameter space for a driven damped oscillator in a double-well potential.
- Modeling and simulation of a network of delay-coupled modified Duffing oscillators.
- Investigation of infinite-range pseudoinverse delayed interactions within the network.
Main Results:
- The network exhibits chaotic dynamics, characterized by randomly frozen amplitudes for individual oscillators.
- A phenomenon of randomly broken global symmetry occurs simultaneously with the freezing of each degree of freedom.
- Exponentially many randomly frozen chaotic attractors, scaling with network size, are observed.
Conclusions:
- Delay-coupled oscillator networks can display complex emergent chaotic behavior through random freezing of individual dynamics.
- The study reveals a novel mechanism for generating numerous coexisting attractors linked to broken global symmetry.
- Findings provide insights into the fundamental principles governing complex network dynamics and emergent chaos.
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