Inducing stable spiral structures and population diversity in the asymmetric May--Leonard model

We study the spiral induction on a two-dimensional lattice using Monte Carlo simulations of the three-species May-Leonard model with asymmetric predation rates. Strongly asymmetric predation rates lead to rapid extinction of two species from three-species coexistence. For weakly asymmetric predation rates, only a fraction of ensembles lead to three-species coexistence. However, when spatially coupled to a symmetric May-Leonard patch, the stable spiral patterns from this region induce quasi-stationary spiral patterns in the asymmetric region. We qualitatively describe the spiral stabilization in the asymmetric patch down to the injection of periodic wavefronts from the adjacent symmetric region. The increase in robustness of stable spiral formation at extreme values of the asymmetric predation rates in the coupled system is compared to the asymmetric May-Leonard model in isolation. We delineate the quasi-stationary nature of coexistence induced in the asymmetric subsystem. In addition to engendering spiral pattern formation, we explore the spiral stability in the asymmetric region and propose a criterion for the quasi-stationary spiral stability of the asymmetric subsystem.