Mathematical analysis on deterministic and stochastic lake ecosystem models

Zhiwei Huang; Gang Huang; Zhiwei Huang; Gang Huang

doi:10.3934/mbe.2019237

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 5: 4723-4740. doi: 10.3934/mbe.2019237

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Mathematical analysis on deterministic and stochastic lake ecosystem models

Zhiwei Huang ,
Gang Huang ^,

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

Received: 27 January 2019 Accepted: 09 May 2019 Published: 27 May 2019

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.
- terrestrial organic matter,
- Lyapunov function,
- Itô’s formula,
- stationary distribution
Citation: Zhiwei Huang, Gang Huang. Mathematical analysis on deterministic and stochastic lake ecosystem models[J]. Mathematical Biosciences and Engineering, 2019, 16(5): 4723-4740. doi: 10.3934/mbe.2019237

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Abstract

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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