Generation and cessation of oscillations: Interplay of excitability and dispersal in a class of ecosystems.

We investigate the complex spatiotemporal dynamics of an ecological network with species dispersal mediated via a mean-field coupling. The local dynamics of the network are governed by the Truscott-Brindley model, which is an important ecological model showing excitability. Our results focus on the interplay of excitability and dispersal by always considering that the individual nodes are in their (excitable) steady states. In contrast to the previous studies, we not only observe the dispersal induced generation of oscillation but also report two distinct mechanisms of cessation of oscillations, namely, amplitude and oscillation death. We show that the dispersal between the nodes influences the intrinsic dynamics of the system resulting in multiple oscillatory dynamics such as period-1 and period-2 limit cycles. We also show the existence of multi-cluster states, which has much relevance and importance in ecology.