상호작용하는 두 생물 종의 개체 수 변화에 대한 수학적 모델

Mathematical models for population changes of two interacting species

  • 심성아 (성신여자대학교 수학과)
  • Shim, Seong-A (Department of Mathematics, Sungshin women's University)
  • 투고 : 2011.12.13
  • 심사 : 2012.01.30
  • 발행 : 2012.02.28

초록

최근 그 중요성이 인식되면서 수학에서 뿐만 아니라, 생물학, 의학, 면역학 등의 여러 분야에서 세계적으로 광범위하게 연구되어지고 있는 수리 생물학(Mathematical biology) 분야의 학문적 시초이며 그 기초를 제공하는 개체 수 생태학 (population ecology) 은 생물 종 (種) 의 개체 수가 서식지 안의 특정 위치에서 시간에 따라 어떻게 변하는 지를 연구하는 분야이다. 이 논문에서는 두 종류의 생물 종이 한 서식지 안에서 상호작용하는 형태로서 포식자-먹이 관계, 경쟁관계, 협력관계를 나타내는 모델들을 살펴본다.

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.

키워드

참고문헌

  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. https://doi.org/10.4039/Ent91293-5
  4. C. Holling,"The characteristics of simple type of predation and parasitism", Canadian Entomologist 91, (1959), pp. 385-398. https://doi.org/10.4039/Ent91385-7
  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. https://doi.org/10.1098/rspa.1927.0118
  7. W.O. Kermack and A.G. McKendrick,"A Contribution to the Mathematical Theory of Epidemics", Proc. Roy. Soc. A, 138, (1932), pp. 55-83. https://doi.org/10.1098/rspa.1932.0171
  8. W.O. Kermack and A.G. McKendrick,"A Contribution to the Mathematical Theory of Epidemics", Proc. Roy. Soc. A, 41, (1933), pp. 94-122.
  9. M. Kot, Elements of Mathematical Ecology, Cambridge University Press, Cambridge, UK, 2001.
  10. A.J. Lotka, Elements of Physical Biology, Williams and Wilkins, Baltimore, 1925.
  11. J.D. Murray, Mathematical biology, Springer-Verlag, Heidelberg (1989).
  12. M. Rosenzweig,"Paradox of enrichment: destabilization of exploitation ecosystems in ecological time", Science, 171, (1971), pp. 385-387. https://doi.org/10.1126/science.171.3969.385
  13. S.A. Shim, Hopf Bifurcation Properties of Holling Type Predator-Prey Systems, Honam Mathematical Journal 30, (2008), no. 3, pp. 293-320.
  14. 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.