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Mathematical models for population changes of two interacting species  

Shim, Seong-A (Department of Mathematics, Sungshin women's University)
Publication Information
Journal for History of Mathematics / v.25, no.1, 2012 , pp. 45-56 More about this Journal
Abstract
Mathematical biology has been recognized its importance recently and widely studied in the fields of mathematics, biology, medical sciences, and immunology. Mathematical ecology is an academic field that studies how populations of biological species change as times flows at specific locations in their habitats. It was the earliest form of the research field of mathematical biology and has been providing its basis. This article deals with various form of interactions between two biological species in a common habitat. Mathematical models of predator-prey type, competitive type, and simbiotic type are investigated.
Keywords
mathematical ecology; Lotka-Volterra systems; Kolmogorov models;
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  • Reference
1 F. Brauer and C. Castillo-Chavez, Mathematical Models in Population Biology and Epidemiology, Springer-Verlag, Heidelberg, 2000.
2 H.I. Freedman, Deterministic Mathematical Models in Population Ecology, Marcel Dekker, New York, 1980.
3 C. Holling, The components of predation as revealed by a study of small-mammal predation of the European pine sawfly , Can. Entomol., 91, (1959), pp. 293-320.   DOI
4 C. Holling,"The characteristics of simple type of predation and parasitism", Canadian Entomologist 91, (1959), pp. 385-398.   DOI
5 C. Holling,"The functional response of predators to prey density and its role in mimicry and population regulation ", Mem. Entomol. Soc. Can., 45, (1965), pp. 3-60.
6 W.O. Kermack and A.G. McKendrick,"A Contribution to the Mathematical Theory of Epidemics", Proc. Roy. Soc. A, 115, (1927) pp. 700-721.   DOI
7 M. Kot, Elements of Mathematical Ecology, Cambridge University Press, Cambridge, UK, 2001.
8 A.J. Lotka, Elements of Physical Biology, Williams and Wilkins, Baltimore, 1925.
9 J.D. Murray, Mathematical biology, Springer-Verlag, Heidelberg (1989).
10 M. Rosenzweig,"Paradox of enrichment: destabilization of exploitation ecosystems in ecological time", Science, 171, (1971), pp. 385-387.   DOI
11 S.A. Shim, Hopf Bifurcation Properties of Holling Type Predator-Prey Systems, Honam Mathematical Journal 30, (2008), no. 3, pp. 293-320.
12 V. Volterra, Variations and fluctuations of the number of individuals in animal species living together, 1926. Translated by R.N. Chapman, Animal Ecology, pp. 409-448, McGraw-Hill, New York, 1931.
13 W.O. Kermack and A.G. McKendrick,"A Contribution to the Mathematical Theory of Epidemics", Proc. Roy. Soc. A, 138, (1932), pp. 55-83.   DOI
14 W.O. Kermack and A.G. McKendrick,"A Contribution to the Mathematical Theory of Epidemics", Proc. Roy. Soc. A, 41, (1933), pp. 94-122.