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Competing spatial and temporal instabilities in a globally coupled bistable semiconductor system near a
1Institut fur Theoretische Physik, Technische Universitat Berlin, Hardenbergstrasse 36, D-10623, Berlin, Germany.
Summary
Complex spatiotemporal dynamics emerge in reaction-diffusion models near bifurcation points. These dynamics, including chaos and oscillations, are sensitive to domain shape, differing significantly between 1D and 2D systems.
Area of Science:
- Complex systems science
- Nonlinear dynamics
- Mathematical modeling
Background:
- Reaction-diffusion models exhibit complex spatiotemporal behaviors.
- Bistable systems are crucial for understanding pattern formation and instabilities.
- Understanding instabilities is key to predicting system dynamics.
Purpose of the Study:
- To investigate complex spatiotemporal dynamics in a 2D reaction-diffusion model.
- To identify conditions leading to mixed spatiotemporal modes.
- To clarify the origins of diverse complex dynamics.
Main Methods:
- Analysis of a globally coupled bistable reaction-diffusion model.
- Investigation near a codimension-two bifurcation point.
- Derivation of conditions for mixed spatiotemporal modes.
Main Results:
- Complex dynamics arise from competing spatial and temporal instabilities.
- Observed phenomena include oscillating current filaments, Shil'nikov attractors, and moving fronts.
- Dynamics are robust across various domain sizes but sensitive to shape variations.
Conclusions:
- Codimension-two bifurcations are critical for complex spatiotemporal behavior.
- Domain geometry significantly influences the emergent dynamics.
- Differences between 1D and 2D dynamics are explained by spatial coupling and instabilities.
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