Constructive effects of environmental noise in an excitable prey–predator plankton system with infected prey

Abstract

An excitable model of fast phytoplankton and slow zooplankton dynamics is considered for the case of lysogenic viral infection of the phytoplankton population. The phytoplankton population is split into a susceptible ( S) and an infected ( I) part. Both parts grow logistically, limited by a common carrying capacity. Zooplankton ( Z) is grazing on susceptibles and infected, following a Holling-type III functional response. The local analysis of the S– I– Z differential equations yields a number of stationary and/or oscillatory regimes and their combinations. Correspondingly interesting is the behaviour under multiplicative noise, modelled by stochastic differential equations. The external noise can enhance the survival of susceptibles and infected, respectively, that would go extinct in a deterministic environment. In the parameter range of excitability, noise can induce prey–predator oscillations and coherence resonance (CR). In the spatially extended case, synchronized global oscillations can be observed for medium noise intensities. Higher values of noise give rise to the formation of stationary spatial patterns.