A minimal model of pattern formation in a prey-predator system
Mathematical and Computer Modelling: An International Journal
| Hi-index | 0.98 |
An excitable model of phytoplankton-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 spatiotemporal behaviour, modelled by stochastic reaction-diffusion equations. Spatial spread or suppression of infection will be presented just as well as competition of concentric and/or spiral population waves for space. The external noise can enhance the survival and spread of susceptibles and infected, respectively, that would go extinct in a deterministic environment. In the parameter range of excitability, noise can induce local blooms of susceptibles and infected.