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Synchronization and coarsening (without self-organized criticality) in a forest-fire model
K E Chan1, P L Krapivsky, S Redner
1Center for BioDynamics, Center for Polymer Studies, and Department of Physics, Boston University, Boston, Massachusetts 02215, USA.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 21, 2002
Summary
This study models forest fire dynamics, showing forests self-organize into synchronized patches. Average patch length grows linearly over time, revealing predictable patterns in forest regrowth and fire cycles.
Area of Science:
- Ecological modeling
- Statistical physics
- Dynamical systems
Background:
- Forest ecosystems exhibit complex dynamics influenced by growth and disturbances.
- Understanding long-term patterns in forest fires is crucial for ecological management.
Purpose of the Study:
- To investigate the long-time dynamics of a forest-fire model.
- To analyze the self-organization and scaling behavior of forest patches.
- To compare numerical simulations with theoretical predictions.
Main Methods:
- Deterministic modeling of tree growth.
- Stochastic modeling of lightning strikes causing instantaneous forest fires.
- Development of an event-driven cluster algorithm for one-dimensional systems.
- Mean-field rate equation analysis.
Main Results:
- The forest-fire model asymptotically organizes into a coarsening, self-similar mosaic of synchronized patches.
- Average patch length (
) exhibits linear growth over time (t → ∞). - Patch number density N(L,t) follows a scaling law
-2N(L/ ), with specific decay functions at small and large scales.
Conclusions:
- The system demonstrates predictable patch coarsening behavior.
- Numerical results align with mean-field predictions for asymptotic dynamics.
- The model provides insights into self-organized criticality in ecological systems.
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