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Zooplankton mortality and the dynamical behaviour of plankton population models

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Abstract

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.

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Authors and Affiliations

  1. Biology Department, Woods Hole Oceanographic Institution, Woods Hole, MA, 02543, USA

    Andrew M. Edwards

  2. Department of Applied Mathematical Studies and Centre for Nonlinear Studies, University of Leeds, Leeds, LS2 9JT, UK

    Andrew M. Edwards & John Brindley

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  1. Andrew M. Edwards
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  2. John Brindley
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Correspondence to Andrew M. Edwards.

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Edwards, A.M., Brindley, J. Zooplankton mortality and the dynamical behaviour of plankton population models. Bull. Math. Biol. 61, 303–339 (1999). https://doi.org/10.1006/bulm.1998.0082

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  • DOI: https://doi.org/10.1006/bulm.1998.0082

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