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

Abstract

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 we 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 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.Species dispersal among connected habitats often identifies the complex spatial dynamics of ecological system and significantly increases the persistence of ecological communities for longer time. Various dynamical models have been used to describe the effect of dispersal in connected habitats. As far as ecological models are concerned, sometimes there exists slow-fast time scales with very interesting dynamics. For example, in aquatic ecosystem, plankton bloom is a result of sudden changes in environmental fluctuations that makes plankton ecosystem as excitable media. Take this into account, the effect of dispersal in slow-fast dynamical ecological system is analyzed qualitatively using mean-field assumption as an external force. In a homogeneous environmental set up, the coupled slow-fast system shows multiple characteristics of sensitivity in synchronized oscillations for different initial density.