- Volume 27 Issue 3
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A Historical Review on Discrete Models of Population Changes and Illustrative Analysis Methods Using Computer Softwares
개체 수 변화에 대한 이산적 모델의 역사적 개요와 컴퓨터 소프트웨어를 이용하는 시각적 분석 방법
- Shim, Seong-A (Dept. of Math., Sungshin Women's Univ.)
- Received : 2014.04.10
- Accepted : 2014.06.10
- Published : 2014.06.30
Species like insects and fishes have, in many cases, non-overlapping time intervals of one generation and their descendant one. So the population dynamics of such species can be formulated as discrete models. In this paper various discrete population models are introduced in chronological order. The author's investigation starts with the Malthusian model suggested in 1798, and continues through Verhulst model(the discrete logistic model), Ricker model, the Beverton-Holt stock-recruitment model, Shep-herd model, Hassell model and Sigmoid type Beverton-Holt model. We discuss the mathematical and practical significance of each model and analyze its properties. Also the stability properties of stationary solutions of the models are studied analytically and illustratively using GSP, a computer software. The visual outputs generated by GSP are compared with the analytical stability results.
- population dynamics;
- discrete models;
- cobweb diagram;
- discrete logistic model;
- the Beverton-Holt stock-recruitment model;
- Ricker model;
- Shepherd model;
- Hassell model;
- Sigmoid type Beverton-Holt model
Supported by : Sungshin Women's University
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