A stochastic analysis of the spatially extended May-Leonard model
arXiv:1706.00309 · doi:10.1088/1751-8121/aa87a8
Abstract
Numerical studies of the May-Leonard model for cyclically competing species exhibit spontaneous spatial structures in the form of spirals. It is desirable to obtain a simple coarse-grained evolution equation describing spatio-temporal pattern formation in such spatially extended stochastic population dynamics models. Extending earlier work on the corresponding deterministic system, we derive the complex Ginzburg-Landau equation as the effective representation of the fully stochastic dynamics of this paradigmatic model for cyclic dominance near its Hopf bifurcation, and for small fluctuations in the three-species coexistence regime. The internal stochastic reaction noise is accounted for through the Doi-Peliti coherent-state path integral formalism, and subsequent mapping to three coupled non-linear Langevin equations. This analysis provides constraints on the model parameters that allow time scale separation and in consequence a further reduction to just two coarse-grained slow degrees of freedom.
arXiv comment17 pages, 1 figure, to appear in J. Phys. A: Math. Theor
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