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Minimal Model of Plankton Systems Revisited with Spatial Diffusion and Maturation Delay
Jiantao Zhao1,2, Jianjun Paul Tian3, Junjie Wei4
1Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, Heilongjiang, People's Republic of China.
Bulletin of Mathematical Biology
|March 4, 2016
Summary
This study examines plankton ecosystem dynamics, revealing how nutrient levels, fish predation, and zooplankton maturation delays influence population stability and introduce new phenomena like oscillations and collapses. Eutrophic conditions generally prevent collapse.
Area of Science:
- Ecological modeling
- Plankton dynamics
- Mathematical biology
Background:
- Revisiting Scheffer's minimal plankton model.
- Incorporating spatial diffusion and maturation delays.
- Investigating nutrient and predation effects.
Purpose of the Study:
- Deepen understanding of plankton system dynamics.
- Explore new phenomena from spatial diffusion and delays.
- Analyze nutrient and fish predation impacts.
Main Methods:
- Mathematical analysis of a plankton model.
- Global stability analysis of equilibria.
- Hopf bifurcation analysis.
Main Results:
- Zooplankton collapse at low nutrients; phytoplankton reach carrying capacity.
- Coexistent equilibria or oscillations emerge with increased nutrients.
- Phytoplankton density increases, zooplankton decreases with higher fish predation.
- System remains stable under eutrophic conditions unless fish predation is extreme.
- Bifurcation analysis reveals complex dynamics based on delay and predation.
Conclusions:
- Nutrient levels, zooplankton maturation delays, and fish predation critically shape plankton ecosystem stability.
- Eutrophic conditions offer resilience against population collapse.
- Complex dynamical patterns, including oscillations, arise from the interplay of model parameters.
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