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Spatial rock-paper-scissors models with inhomogeneous reaction rates
Qian He1, Mauro Mobilia, Uwe C Täuber
1Department of Physics and Center for Stochastic Processes in Science and Engineering, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061-0435, USA. heq07@vt.edu
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 15, 2011
Summary
The rock-paper-scissors game, even with variations like spatial disorder, shows stable species coexistence. Stochastic fluctuations and spatial correlations have minimal impact on these cyclic predator-prey models.
Area of Science:
- Complex Systems
- Theoretical Ecology
- Statistical Physics
Background:
- Cyclic predator-prey models, like the rock-paper-scissors game, exhibit complex dynamics.
- Understanding species coexistence in spatially extended systems is crucial for ecological theory.
- Stochasticity and spatial heterogeneity can significantly alter population dynamics.
Purpose of the Study:
- Investigate the impact of spatial variability and site restrictions on rock-paper-scissors game dynamics.
- Analyze transient oscillations and spatial correlations in three-species predator-prey models.
- Determine the robustness of the rock-paper-scissors system to model variations.
Main Methods:
- Monte Carlo simulations on one- and two-dimensional lattices.
- Analysis of transient oscillations in species densities.
- Calculation of spatial correlation functions in the quasistationary state.
Main Results:
- Quenched disorder in reaction rates has minimal effect on dynamics and coexistence.
- Site occupancy restrictions show only a minor influence on system properties.
- Extinction times in small systems were numerically determined.
Conclusions:
- The spatial rock-paper-scissors system is remarkably robust to model variations.
- Stochastic fluctuations and spatial correlations play a minor role in the system's long-time behavior.
- Cyclic competition models demonstrate stable coexistence despite environmental heterogeneity.
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