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Defect-mediated turbulence and transition to spatiotemporal intermittency in the Gray-Scott model
Igal Berenstein1, Yannick De Decker1
1NonLinear Physical Chemistry Unit, and Interdisciplinary Center for Nonlinear Phenomena and Complex Systems (CENOLI), Université libre de Bruxelles (ULB), Campus Plaine, C.P. 231. B-1050 Brussels, Belgium.
Chaos (Woodbury, N.Y.)
|January 3, 2015
Summary
The Gray-Scott model generates defect-mediated turbulence near the Andronov homoclinic bifurcation. Further parameter changes transition turbulence into spatiotemporal intermittency via a stable node.
Area of Science:
- Chemical reactions and pattern formation
- Nonlinear dynamics and chaos theory
Background:
- The Gray-Scott model is a reaction-diffusion system known for complex pattern formation.
- Understanding the transition from turbulent behavior to other dynamic regimes is crucial in nonlinear systems.
Purpose of the Study:
- To investigate the emergence of defect-mediated turbulence in the Gray-Scott model.
- To characterize the transition from defect-mediated turbulence to spatiotemporal intermittency.
Main Methods:
- Analysis of the Gray-Scott model dynamics.
- Identification of bifurcations including Hopf and Andronov homoclinic bifurcations.
- Examination of system behavior across a range of control parameters.
Main Results:
- Defect-mediated turbulence arises from the limit cycle preceding the Andronov homoclinic bifurcation.
- As the control parameter is altered, the system increasingly visits a stable node.
- This transition leads to a gradual shift from defect-mediated turbulence to spatiotemporal intermittency.
Conclusions:
- The Gray-Scott model exhibits a clear pathway from turbulence to intermittency.
- Bifurcation analysis is key to understanding these complex dynamic transitions.
- The findings provide insights into pattern evolution in reaction-diffusion systems.
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