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Oscillatory and chaotic dynamics in compartmentalized geometries
Francisco Chávez1, Raymond Kapral
1Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario, Canada M5S 3H6.
Summary
Spatial compartmentalization of chemical reactions can induce complex dynamics like oscillations and chaos. Changing system size and domain geometry can control these behaviors, leading to bifurcations in reaction-diffusion systems.
Area of Science:
- Chemical Kinetics
- Nonlinear Dynamics
- Mathematical Chemistry
Background:
- The Willamowski-Rössler model exhibits oscillations and chaotic dynamics under mass action kinetics.
- Spatial effects in chemical reactions can significantly alter system behavior.
Purpose of the Study:
- To investigate how spatial compartmentalization influences the dynamics of a multistep reaction mechanism.
- To explore the impact of system size and domain geometry on reaction-diffusion systems.
Main Methods:
- Decomposing the reaction mechanism into spatially distinct domains.
- Coupling these domains via diffusion.
- Analyzing spatiotemporal states using simulations of reaction-diffusion equations and integral equations.
Main Results:
- Compartmentalization with simple steady states in isolated domains can lead to bifurcations.
- Changes in system size and domain geometry can induce simple oscillations, period-doubled oscillations, and chaotic states.
- Demonstrated control over complex dynamics through spatial arrangement.
Conclusions:
- Spatial compartmentalization is a critical factor in determining the emergent dynamics of chemical reaction systems.
- System size and geometric arrangement offer tunable parameters for controlling complex behaviors in reaction-diffusion systems.