Persistence and periodic orbits for two-species non-autonomous diffusion Lotka-Volterra models
A nonautonomous competition system is investigated. The species \(x\) can diffuse between two patches of a heterogeneous environment with barriers between patches, but for the competitor species \(y\), the diffusion does not involve a barrier between patches. It is assumed that all parameters are time-dependent. It is shown that the system can be made persistent under some appropriate conditions. Sufficient conditions that guarantee the existence of a unique positive periodic orbit which is globally asymptotic stable are derived.
scientific article; zbMATH DE number 2151006