A Simple Plankton Model with Complex Behaviour

In this paper we extend the \(P_{1}P_{2}ZN\) model, introduced by Cropp and Norbury (J Plankton Res 31:939–963, 2009) to investigate the effects of specialist (or discriminate) and generalist (or indiscriminate) grazing (as parameterised by ρ) on a prey-prey-predator model for plankton, in the presence of a limiting nutrient. We also examine the influence of facultative and obligate omnivory on the survival of Z as a generalist predator, as we vary the linear mortality parameter \(\sigma _{Z}\). This leads to bifurcation transition diagrams, which also include steady state stability branches for certain critical points. For specialist grazing (ρ = 0) the bifurcation transition diagram shows steady states, periodic and chaotic dynamics, with very small windows of periodic behaviour, as \(\sigma _{Z}\) varies, while for generalist grazing (ρ = 1), we only find periodic or steady state behaviours. The dynamics is interpretable in terms of facultative/obligate omnivory of Z. Results suggest that green ocean plankton code in global climate change modelling might run more stably with generalist grazing terms and careful control of grazer mortality.