We investigate the dynamical behaviour of a simple plankton population model, which explicitly simulates the concentrations of nutrient, phytoplankton and zooplankton in the oceanic mixed layer. The model consists of three coupled ordinary differential equations. We use analytical and numerical techniques, focusing on the existence and nature of steady states and unforced oscillations (limit cycles) of the system. The oscillations arise from Hopf bifurcations, which are traced as each parameter in the model is varied across a realistic range. The resulting bifurcation diagrams are compared with those from our previous work, where zooplankton mortality was simulated by a quadratic function-here we use a linear function, to represent alternative ecological assumptions. Oscillations occur across broader ranges of parameters for the linear mortality function than for the quadratic one, although the two sets of bifurcation diagrams show similar qualitative characteristics. The choice of zooplankton mortality function, or closure term, is an area of current interest in the modelling community, and we relate our results to simulations of other models.

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We examine the qualitative behaviour of an NPZ (nutrient-phytoplankton-zooplankton) model for parameter ranges consistent with values used in the literature. The wide range of values partly reflects variations of conditions in dzrerent eizair~lzl?zcnts~k : , $e p k n k~m , bur i~ % m y cnsex is rr measure of the dzficulties in making observations and consequent uncertainties. We pay particular attention to the bifurcational behaviour of the system, and to the regions of parameter space for which oscillatoy r I ....'.'. u~, t~-~~~~~ ;~ssi5!:;:s.l .h ncci??ccn_~ h~hnwnur has recently been found in both observational data and in more complex ecosystem models. In some regions of parameter space, we also find that multiple attractors occur. Finally, we examine in more detail the behaviour for a range of values of nutrient input.

We consider a system of partial differential equations describing two spatially distributed populations in a "predator-prey" interaction with each other. The spatial evolution is governed by three processes: positive taxis of predators up the gradient of prey (pursuit), negative taxis of prey down the gradient of predators (evasion), and diffusion resulting from random motion of both species. We demonstrate a new type of propagating wave in this system. The mechanism of propagation of these waves essentially depends on the taxis and is entirely different from waves in a reaction-diffusion system. Unlike typical reaction-diffusion waves, which annihilate on collision, these "taxis" waves can often penetrate through each other and reflect from impermeable boundaries.