Effect of migration on Host-Parasitoid Outbreaks

Spatial coupling in dynamical systems undergoing a stable cycle is known to generate a myriad of phase locking behaviors. In the context of ecological populations, phase locking could have both beneficial and detrimental consequences. Synchronized populations are more prone to simultaneous extinction under severe external conditions, like weather, thus making it important to study the conditions leading to phase locking. Here, we introduce a simple discrete time model for a host-parasitoid system with spatial coupling. We explore how migration affects the dynamics of individual oscillators as well as phase locking patterns. Our model by design, has an inherent time lag between the onset and the effects of migration and thus could be relevant more generally in the field of spatially coupled dynamical systems with inherent time lag.