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From Turing patterns to chimera states in the 2D Brusselator model
1Institute of Nanoscience and Nanotechnology, National Center for Scientific Research "Demokritos," 15341 Athens, Greece.
Chaos (Woodbury, N.Y.)
|April 1, 2023
Summary
The Brusselator model, when nonlocally coupled, can generate Turing patterns or chimera states. Tuning coupling parameters transitions the system between stable spatial patterns and dynamic spatiotemporal chaos.
Area of Science:
- Chemical kinetics
- Nonlinear dynamics
- Pattern formation
Background:
- The Brusselator model is a key prototype for autocatalytic reactions, notably the Belousov-Zhabotinsky reaction.
- Diffusively coupled Brusselators exhibit Turing bifurcations, forming spatial patterns like spots, stripes, and spirals.
Purpose of the Study:
- To investigate pattern formation in nonlocally coupled Brusselator systems.
- To explore the transition from Turing patterns to chimera states by varying coupling parameters.
Main Methods:
- Utilized generic nonlocally coupled Brusselator models.
- Analyzed system behavior across a range of coupling strengths (R).
- Identified parameter regimes leading to Turing patterns and chimera states.
Main Results:
- Classical Turing patterns are recovered in the diffusive limit (R→1).
- Chimera states emerge for intermediate coupling ranges and specific parameter values.
- Demonstrated a transition from stable Turing structures to spatiotemporal chimera states.
Conclusions:
- Nonlocal coupling in the Brusselator system allows for a rich variety of spatio-temporal dynamics.
- System parameters can be tuned to switch between ordered Turing patterns and complex chimera states.
- This work provides insights into pattern formation and emergent behavior in nonlinear systems.
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