Journal of the Korean Society for Industrial and Applied Mathematics

  • 제15권2호
  • /
  • Pages.137-142
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  • 2011
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  • 1226-9433(pISSN)
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  • 1229-0645(eISSN)
한국산업응용수학회 (Korean Society for Industrial and Applied Mathematics)
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PREDATOR-PREY IN PATCHY SPACE WITH DIFFUSION

  • Alb, Shaban (DEPARTMENT OF MATHEMATICS, FACULTY OF SCIENCE, AL-AZHAR UNIVERSITY)
  • 투고 : 2010.12.28
  • 심사 : 2011.05.15
  • 발행 : 2011.06.25
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초록

In this paper we formulate a predator-prey system in two patches in which the per capita migration rate of each species is influenced only by its own density, i.e. there is no response to the density of the other one. Numerical studies show that at a critical value of the bifurcation parameter the system undergoes a Turing bifurcation, i. e. the stable constant steady state loses its stability and spatially non-constant stationary solutions, a pattern emerge.

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참고문헌

  1. Farkas M. Dynamical Models in Biology, Academic Press, 2001.
  2. Huang Y., Diekmann O. Interspecific influence on mobility and Turing instability, Bull. Math. Biol. 65 (2003) 143-156. https://doi.org/10.1006/bulm.2002.0328
  3. Murray J. D. Mathematical Biology, Berlin, Springer-Verlag, 1989.
  4. Takeuchi Y. Global Dynamical Properties of Lotka-Volterra Systems, World Scientific, 1996.
  5. Turing A. M. The chemical basis of morphogenesis, Philos. Trans. Roy. Soc. London B237, (1953) 37-72, reprinted: Bull. Math. Biol. 52 (1990) 153-197.