EPL 102 (2013) 28012.
When does cyclic dominance lead to stable spiral waves?
Alastair M. Rucklidge
Department of Applied Mathematics,
University of Leeds, Leeds, LS2 9JT, UK
Species diversity in ecosystems is often accompanied by characteristic
spatio-temporal patterns. Here, we consider a generic two-dimensional
population model and study the spiraling patterns arising from the combined
effects of cyclic dominance of three species, mutation, pair-exchange and
individual hopping. The dynamics is characterized by nonlinear mobility and a
Hopf bifurcation around which the system's four-phase state diagram is inferred
from a complex Ginzburg-Landau equation derived using a perturbative multiscale
expansion. While the dynamics is generally characterized by spiraling patterns,
we show that spiral waves are stable in only one of the four phases.
Furthermore, we characterize a phase where nonlinearity leads to the
annihilation of spirals and to the spatially uniform dominance of each species
in turn. Away from the Hopf bifurcation, when the coexistence fixed point is
unstable, the spiraling patterns are also affected by the nonlinear diffusion.
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