  We study the induction and stabilization of spiral structures for the cyclic
three-species stochastic May-Leonard model with asymmetric predation rates on a
spatially inhomogeneous two-dimensional toroidal lattice using Monte Carlo
simulations. In an isolated setting, strongly asymmetric predation rates lead
to rapid extinction from coexistence of all three species to a single surviving
population. Even for weakly asymmetric predation rates, only a fraction of
ecologies in a statistical ensemble manages to maintain full three-species
coexistence. However, when the asymmetric competing system is coupled via
diffusive proliferation to a fully symmetric May-Leonard patch, the stable
spiral patterns from this region induce transient plane-wave fronts and
ultimately quasi-stationary spiral patterns in the vulnerable asymmetric
region. Thus the endangered ecological subsystem may effectively become
stabilized through immigration from even a much smaller stable region. To
describe the stabilization of spiral population structures in the asymmetric
region, we compare the increase in the robustness of these topological defects
at extreme values of the asymmetric predation rates in the spatially coupled
system with the corresponding asymmetric May-Leonard model in isolation. We
delineate the quasi-stationary nature of coexistence induced in the asymmetric
subsystem by its diffusive coupling to a symmetric May-Leonard patch, and
propose a (semi-)quantitative criterion for the spiral oscillations to be
sustained in the asymmetric region.
