Stability Analysis of a Three-Species, Multi-Patch Variant of the Lotka-Volterra Model

We investigate the stability of the steady-state behavior of a variant of the classic Lotka-Volterra predator-prey model. The variant, LV(3,n), involves three interacting species distributed among n patches with diffusive interaction between the patches; one of the species is allowed to migrate between adjacent patches. Criteria on the phase-space of the three interaction constants are determined to ensure stability of the population steady-states.