Mathematical analysis on deterministic and stochastic lake ecosystem models | Zendy

Zhiwei Huang | Zendy; Gang Huang | Zendy

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Mathematical analysis on deterministic and stochastic lake ecosystem models

Author(s) -

Zhiwei Huang,

Gang Huang

Publication year - 2019

Publication title -

mathematical biosciences and engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.451

H-Index - 45

eISSN - 1551-0018

pISSN - 1547-1063

DOI - 10.3934/mbe.2019237

Subject(s) - ergodic theory , lyapunov function , ecosystem , zooplankton , statistical physics , population , invariance principle , plankton , stochastic modelling , ecology , stochastic process , mathematics , physics , statistics , biology , mathematical analysis , linguistics , philosophy , demography , quantum mechanics , nonlinear system , sociology

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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