Effect of light on the growth of non-nitrogen-fixing and nitrogen-fixing phytoplankton in an aquatic system. (English) Zbl 1341.34055
Summary: We discuss a mathematical model of growth of two types of phytoplankton, non-nitrogen-fixing and nitrogen-fixing, that both require light in order to grow. We use general functional responses to represent the inhibitory effect their biomass has on the exposure to light. We give conditions for the existence and local stability of all of the possible steady-states (die out, single species survival, and coexistence). We derive conditions for global stability of the die out and single-species steady-states and for persistence of both species when the coexistence steady-state exists. Numerical investigation illustrates the qualitative dynamics demonstrating that even under constant environmental conditions, both stable intrinsic oscillatory behavior and a period doubling route to chaotic dynamics are possible. We also show that competitor-mediated coexistence can occur due to the positive feedback resulting from recycling by the nitrogen-fixing phytoplankton. To show the impact of seasonal change in water depth, we also allow the water depth to vary in an annual cycle and discuss echo blooms in this context.
MSC:
| 34C60 | Qualitative investigation and simulation of ordinary differential equation models |
| 34D20 | Stability of solutions to ordinary differential equations |
| 34D05 | Asymptotic properties of solutions to ordinary differential equations |
| 92D25 | Population dynamics (general) |
| 34C23 | Bifurcation theory for ordinary differential equations |
| 34C05 | Topological structure of integral curves, singular points, limit cycles of ordinary differential equations |
| 34C28 | Complex behavior and chaotic systems of ordinary differential equations |
Keywords:
phytoplankton; non-nitrogen/nitrogen fixation; trichodesmium; nutrient; light; stability; steady-state; Hopf and period doubling bifurcations; oscillatory behaviour; chaotic dynamics; competitor-mediated coexistence; echo bloomsSoftware:
XPPAUTReferences:
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