Zooplankton mortality and the dynamical behaviour of plankton population models
 Andrew M. Edwards,
 John Brindley
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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 previouswork, 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.
 Title
 Zooplankton mortality and the dynamical behaviour of plankton population models
 Journal

Bulletin of Mathematical Biology
Volume 61, Issue 2 , pp 303339
 Cover Date
 199903
 DOI
 10.1006/bulm.1998.0082
 Print ISSN
 00928240
 Online ISSN
 15229602
 Publisher
 SpringerVerlag
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 Authors

 Andrew M. Edwards ^{(1)} ^{(2)}
 John Brindley ^{(2)}
 Author Affiliations

 1. Biology Department, Woods Hole Oceanographic Institution, Woods Hole, MA, 02543, USA
 2. Department of Applied Mathematical Studies and Centre for Nonlinear Studies, University of Leeds, Leeds, LS2 9JT, UK