A Simple Plankton Model with Complex Behaviour

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Author(s)
Moroz, IM
Cropp, R
Norbury, J
Griffith University Author(s)
Year published
2016
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In this paper we extend the P1P2ZN 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 σZ . This leads to bifurcation transition diagrams, which also include steady state stability branches for certain critical points. For specialist grazing ...
View more >In this paper we extend the P1P2ZN 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 σZ . 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 σZ 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.
View less >
View more >In this paper we extend the P1P2ZN 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 σZ . 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 σZ 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.
View less >
Book Title
The Foundations of Chaos Revisited: From Poincare to Recent Advancements
Copyright Statement
© 2016 Springer. This is the author-manuscript version of this paper. It is reproduced here in accordance with the copyright policy of the publisher. Please refer to the publisher’s website for further information.
Subject
Other environmental sciences not elsewhere classified