Mathematical Modelling of Population Growth: The Case of Logistic and Von Bertalanffy Models  

作　　者：Mohammed Yiha Dawed Purnachandra Rao Koya Ayele Taye Goshu 

机构地区：[1]School of Mathematical and Statistical Sciences, Hawassa University, Hawassa, Ethiopia

出　　处：《Open Journal of Modelling and Simulation》2014年第4期113-126,共14页建模与仿真（英文）

摘　　要：In this paper, some theoretical mathematical aspects of the known predator-prey problem are considered by relaxing the assumptions that interaction of a predation leads to little or no effect on growth of the prey population and the prey growth rate parameter is a positive valued function of time. The predator growth model is derived considering that the prey follows a known growth models viz., Logistic and Von Bertalanffy. The result shows that the predator’s population growth models look to be new functions. For either models, the predator population size either converges to a finite positive limit or to 0 or diverges to +∞. It is shown algebraically and illustrated pictorially that there is a condition at which the predator-prey population models both converge to the same finite limit. Derivations and simulation studies are provided in the paper. Analysis of equilibrium points and stability is also included.In this paper, some theoretical mathematical aspects of the known predator-prey problem are considered by relaxing the assumptions that interaction of a predation leads to little or no effect on growth of the prey population and the prey growth rate parameter is a positive valued function of time. The predator growth model is derived considering that the prey follows a known growth models viz., Logistic and Von Bertalanffy. The result shows that the predator’s population growth models look to be new functions. For either models, the predator population size either converges to a finite positive limit or to 0 or diverges to +∞. It is shown algebraically and illustrated pictorially that there is a condition at which the predator-prey population models both converge to the same finite limit. Derivations and simulation studies are provided in the paper. Analysis of equilibrium points and stability is also included.

关 键 词：PREDATOR-PREY Koya-Goshu LOGISTIC POPULATION GROWTH Von BERTALANFFY 

分 类 号：O1[理学—数学]