Journal of the Korean Society for Industrial and Applied Mathematics

  • 제13권1호
  • /
  • Pages.21-29
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  • 2009
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  • 1226-9433(pISSN)
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  • 1229-0645(eISSN)
한국산업응용수학회 (Korean Society for Industrial and Applied Mathematics)
권호 표지

INSTABILITY IN A PREDATOR-PREY MODEL WITH DIFFUSION

  • Aly, Shaban (DEPT OF MATHEMATICS, FACULTY OF SCIENCE, KING KHALID UNIV.)
  • 투고 : 2009.01.16
  • 심사 : 2009.02.20
  • 발행 : 2009.03.25
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초록

This paper treats the conditions for the existence and stability properties of stationary solutions of a predator-prey interaction with self and cross-diffusion. We show that at a certain critical value a diffusion driven instability occurs, i.e. the stationary solution stays stable with respect to the kinetic system (the system without diffusion) but becomes unstable with respect to the system with diffusion and that Turing instability takes place. We note that the cross-diffusion increase or decrease a Turing space (the space which the emergence of spatial patterns is holding) compared to the Turing space with self-diffusion, i.e. the cross-diffusion response is an important factor that should not be ignored when pattern emerges.

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참고문헌

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