Induction of spatio-temporal spiral defects in an inhomogeneous stochastic May-Leonard system

We study the induction of spiral defects in an inhomogeneous two-dimensional Monte Carlo toroidal lattice simulation of the stochastic three-species May-Leonard model with asymmetric predation rates. In an isolated setting, strongly asymmetric predation rates cause fast extinction from coexistence of all three species to a single surviving population. However, when spatially coupled to a fully symmetric May-Leonard patch, the spiral patterns from this stable region induce transient plane wave fronts and ultimately quasi-stationary spiral patterns in the asymmetric region. We quantitatively analyze the initial injection of plane wave fronts from the symmetric region and the subsequent formation of spirals, and explore the conditions for the stabilization of the weaker ecosystem. To this end, we study characteristic correlation lengths and oscillation frequencies, the shape and size of the spirals induced in the asymmetric region in comparison to the isotropic spirals in the symmetric regime, and the effects of varying system size and individuals' mobility.