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06:55
Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
Published on: September 26, 2016
Pattern formation in forced reaction diffusion systems with nearly degenerate bifurcations.
José Halloy1, Giorgio Sonnino, Pierre Coullet
1Service of Social Ecology, Université Libre de Bruxelles (U.L.B.), Boulevard du Triomphe, Campus de la Plaine, C.P. 231, Building NO, Brussels B-1050, Belgium. jhalloy@ulb.ac.be
Chaos (Woodbury, N.Y.)
|October 2, 2007
Summary
This study reports stable standing-wave patterns in generic oscillators using complex Ginzburg-Landau equations. Researchers discovered new mixed-mode solutions arising from parametric forcing near bifurcations.
Area of Science:
- Nonlinear dynamics
- Pattern formation in dissipative systems
- Mathematical physics
Background:
- Generic oscillators are fundamental in modeling complex systems.
- Parametric forcing can induce novel dynamic behaviors.
- Turing-Hopf bifurcations are critical points in system stability.
Purpose of the Study:
- To investigate the existence and stability of standing-wave patterns in parametrically forced dissipative oscillators.
- To elucidate the mechanism of dispersion-induced patterns near degenerate Turing-Hopf bifurcations.
- To identify and characterize new types of stable standing-wave structures.
Main Methods:
- Analysis of coupled complex Ginzburg-Landau equations.
- Investigation of systems near degenerate Turing-Hopf bifurcations.
- Utilizing the Brussellator model as a specific case study.
Main Results:
- Demonstrated the existence and stability of standing-wave patterns.
- Illustrated the mechanism of dispersion-induced pattern formation.
- Identified novel mixed-mode solutions occurring between Turing and Hopf instabilities.
Conclusions:
- Parametric forcing of dissipative oscillators can lead to stable standing-wave patterns.
- Mixed-mode solutions represent a new class of stable structures in these systems.
- The findings provide insights into pattern formation in nonlinear systems.
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