Speaker
Description
A metapopulation model describes local populations of interacting species distributed across discrete habitat patches connected through migration. In this work, the local dynamics within each patch are modeled by May--Leonard Competitive Lotka--Volterra (MLCLV) systems consisting of three species, whose pairwise competitive interactions are encoded by a circulant interaction matrix. Such systems model cyclic competition among three species, and the interaction coefficients describing the mutual inhibitory effects in pairwise competition determine the dynamics of these systems. Depending on the interaction coefficients, MLCLV systems may exhibit stable convergence to the coexistence equilibrium, stable periodic limit cycles, convergence to boundary equilibria, or heteroclinic cycles. We consider $m$ patches, where each patch is inhabited by the same three species, and the local dynamics in each patch are governed by an MLCLV system exhibiting a stable periodic limit cycle. The objective of this work is to ensure asymptotic convergence of the trajectories to the coexistence equilibrium in each patch. We propose a scheme to design a metapopulation network that achieves this control objective across all patches via inter-patch species migration. Using Lyapunov methods coupled with LaSalle's invariance principle, we prove that the resulting metapopulation model admits a unique coexistence equilibrium that is globally asymptotically stable.
