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PREDATOR-PREY IN PATCHY SPACE WITH DIFFUSION

  • Alb, Shaban (DEPARTMENT OF MATHEMATICS, FACULTY OF SCIENCE, AL-AZHAR UNIVERSITY)
  • Received : 2010.12.28
  • Accepted : 2011.05.15
  • Published : 2011.06.25

Abstract

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.

References

  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.