He, Q, Mobilia, M orcid.org/0000-0002-1424-567X and Tauber, UC (2011) Coexistence in the two-dimensional May-Leonard model with random rates. The European Physical Journal B - Condensed Matter and Complex Systems, 82 (1). pp. 97-105. ISSN 1434-6036
Abstract
We employ Monte Carlo simulations to numerically study the temporal evolution and transient oscillations of the population densities, the associated frequency power spectra, and the spatial correlation functions in the (quasi-) steady state in two-dimensional stochastic May-Leonard models of mobile individuals, allowing for particle exchanges with nearest-neighbors and hopping onto empty sites. We therefore consider a class of four-state three-species cyclic predator-prey models whose total particle number is not conserved. We demonstrate that quenched disorder in either the reaction or in the mobility rates hardly impacts the dynamical evolution, the emergence and structure of spiral patterns, or the mean extinction time in this system. We also show that direct particle pair exchange processes promote the formation of regular spiral structures. Moreover, upon increasing the rates of mobility, we observe a remarkable change in the extinction properties in the May-Leonard system (for small system sizes): (1) as the mobility rate exceeds a threshold that separates a species coexistence (quasi-) steady state from an absorbing state, the mean extinction time as function of system size N crosses over from a functional form similar to e (cN) /N (where c is a constant) to a linear dependence; (2) the measured histogram of extinction times displays a corresponding crossover from an (approximately) exponential to a Gaussian distribution. The latter results are found to hold true also when the mobility rates are randomly distributed.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Keywords: | Rock-Paper-Scissors; Lotka-Volterra Model; Game; Biodiversity; Organization; Competition; Strategies; Theoretical Ecology; Complex Systems; Evolutionary dynamics; Mathematical and computational modelling |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 15 Jun 2018 12:52 |
Last Modified: | 15 Jun 2018 12:52 |
Status: | Published |
Publisher: | Springer Nature |
Identification Number: | 10.1140/epjb/e2011-20259-x |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:87675 |