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Travelling chimeras in oscillator lattices with advective-diffusive coupling
L Smirnov1,2, A Pikovsky3
1Department of Control Theory, Research and Education Mathematical Center 'Mathematics for Future Technologies', Nizhny Novgorod State University, Gagarin Avenue 23, Nizhny Novgorod 603022, Russia.
Summary
We introduce advection to coupled phase oscillators, creating moving chimera patterns. These patterns exhibit distinct synchronous and disordered domains, with stable traveling wave solutions found.
Area of Science:
- Nonlinear dynamics
- Complex systems
- Pattern formation
Background:
- Seminal chimera studies considered only diffusion in coupled phase oscillators.
- Previous models lacked asymmetric coupling, limiting pattern dynamics.
Purpose of the Study:
- To investigate the effect of advection on chimera patterns in phase oscillator arrays.
- To explore the emergence of moving, weakly turbulent patterns.
- To identify stable traveling wave solutions in asymmetric systems.
Main Methods:
- Modeling a 1D array of phase oscillators coupled via an auxiliary complex field.
- Introducing advection to create left-right asymmetric coupling.
- Analyzing the emergent patterns, including synchronous and disordered domains.
- Searching for exact traveling wave solutions.
Main Results:
- Advection leads to moving chimera patterns.
- A weakly turbulent moving pattern emerges with distinct synchronous and disordered domains.
- Dense systems show strong local correlations in disordered domains, resembling smooth phase profiles.
- Exact traveling wave chimera-like solutions were found, with varying stability.
Conclusions:
- Asymmetric coupling via advection generates novel, dynamic chimera states.
- Moving chimera patterns exhibit complex spatiotemporal organization.
- The study identifies stable traveling wave solutions, advancing understanding of extended nonlinear systems.
Keywords:
advective–diffusive couplingchimerasoscillatory mediumtravelling wave patternsweak turbulenceMore Related Videos
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