Abstract
The long-time behavior of the consumer population in a Gallopin's system, located in a polluted environment, was studied. Firstly, a mathematical model, i. e., a nonlinear ordinary differential system, was made by taking a constant catch rate into account in model of MA Zhi-en. Secondly, using the extension theorem and the comparison theorem, the bound of the system was estimated. Then, the effect of the pollution on the consumer population was discussed by the use of calculus and qualitative theory of differential equation. Finally, some conditions for weak persistence in the mean and extinction are found out. The threshold between persistence and extinction can be established in some cases.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
HE Ze-rong, MA Zhi-en. On the effect of pollution and catch to a logistic population [J].Journal of Biomathematics, 1997,12(3):230 ∼ 237. (in Chinese)
MA Zhi-en, SONG Bao-jun, Hallam T G. The threshold between persistence and extinction of a population in a polluted environment [J].Bull Math Biol, 1989,51(3):120.
MA Zhi-en.Mathematical Modeling and Study on Population Ecology [M]. Hefei: Anhui Education Press, 1996. (in Chinese)
CHEN Lan-sun.The Models and Researching Methods in Mathematical Ecology [M]. Beijing: Science Press, 1988. (in Chinese)
YOU Bing-li.A Supplementary Texbook on Ordinary Differential Equations [M]. Beijing: People's Education Press, 1981. (in Chinese)
Author information
Authors and Affiliations
Additional information
Communicated by LIN Zong-chi
CLC number: 0175.14
Document code: A
Rights and permissions
About this article
Cite this article
Ze-rong, H., Zhi-en, M. The survival analysis for gallopin' s system in a polluted environment. Appl Math Mech 21, 921–928 (2000). https://doi.org/10.1007/BF02428362
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02428362