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Mathematical analysis on deterministic and stochastic lake ecosystem models

School of Mathematics and Physics, China University of Geosciences, 430074, Wuhan, P.R. China

Special Issues: Differential Equations in Mathematical Biology

In this paper, we propose and study the deterministic and stochastic lake ecosystem models to investigate the impact of terrestrial organic matter upon persistence of the plankton populations. By constructing Lyapunov function and using the LaSalle’s Invariance Principle, we establish global properties of the deterministic model. The dynamical behavior of solutions fits well with some experimental results. It is concluded that the terrestrial organic matter plays an important role in influencing interactions between phytoplankton and zooplankton. Based on the fluctuations of lake ecosystem, we further develop a stochastically perturbed model. Theoretic analysis implies that the stochastic model exists a stationary distribution which is ergodic. The key point of our analysis is to enhance our knowledge of the factors governing the dynamics of plankton population models.
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Keywords terrestrial organic matter; Lyapunov function; Itô’s formula; stationary distribution

Citation: Zhiwei Huang, Gang Huang. Mathematical analysis on deterministic and stochastic lake ecosystem models. Mathematical Biosciences and Engineering, 2019, 16(5): 4723-4740. doi: 10.3934/mbe.2019237

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