Periodic dynamical systems in unidirectional metapopulation models

In periodically varying environments, population models generate periodic dynamical systems. To understand the effects of unidirectional dispersal on local patch dynamics in fluctuating environments, dynamical systems theory is used to study the resulting periodic dynamical systems. In particular, a unidirectional dispersal linked two patch nonautonomous metapopulation model is constructed and used to explain the qualitative dynamics of linked versus unlinked independent patches. As in singlepatch, single-species population models, unidirectional nonautonomous models support multiple attractors where local population models support single attractors.