Dynamic Modeling Of The Effect Of Abiotic Factors On The Growth Of Phytoplankton

In this paper, models of population dynamics are established to examine the effect of abiotic factors on the growth of phytoplankton. The paper starts with introducing the background, methods and results of this study. The study is divided into three parts.A bottom-up nutrient phytoplankton model, which incorporates the combined effects of temperature and light, is proposed and analyzed to explore the dynam-ics of phytoplankton bloom. The population growth model reasonably captures such observed dynamics qualitatively. An ecological reproductive index is defined to characterize the growth of the phytoplankton which also allows a comprehen-sive analysis of the role of temperature and light on the growth and reproductive characteristics of phytoplankton in general. The model provides a framework to study the mechanisms of phytoplankton dynamics in shallow lake and may even be employed to study the controlled phytoplankton bloom.Based on the study of effect of constant abiotic factors on the growth of phy-toplankton, a non-autonomous nutrient-phytoplankton interacting model incor-porating the effect of time-varying temperature is established. The impacts of temperature on metabolism of phytoplankton such as nutrient uptake, death rate,and nutrient releasing from particulate nutrient are investigated. The ecological reproductive index is formulated to present a threshold criteria and to character-ize the dynamics of phytoplankton. The positive invariance, dissipativity, and the existence and stability of boundary and positive periodic solution are established.The analysis relies on the comparison principle, the coincidence degree theory and Lyapunov direct method. The effect of seasonal temperature and daily tempera-ture on phytoplankton biomass axe simulated numerically. Numerical simulation shows that the phytoplankton biomass is very robust to the variation of water temperature. The performance and the adaptability of the model is well assessed by carrying out an application scenario to our field study in Lake Tai in China.The dynamics of the model and model predictions agree well with the experimen-tal data. Our model provides a reasonable explanation of triggering mechanism of phytoplankton bloom.Due to neglecting the effect of element ratio on the growth of phytoplankton,a food chain with two limiting nutrients (carbon and phosphorus) in the form of a stoichiometric population model is fully investigated. This model naturally ex-tends the LKE model due to Loladze, Kuang and Elser. A comprehensive analysis of the rich dynamics of the targeted model is well explored both analytically and numerically. The chaotic dynamic is observed in this simple stoichiometric food chain and is fully investigated. Our finding shows that decreasing producer pro-duction efficiency may have only a small effect on the consumer growth but a more profound impact on the top predator growth indirectly.The paper ends with summarizing the main conclusions of this study. Many related references are listed finally.