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A discrete predator-prey system with age-structurefor predator and naturalbarriers for prey

Published online by Cambridge University Press:  15 April 2002

Sanyi Tang  and
Lansun Chen
Sanyi Tang
Affiliation:
Institute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, P. R. China. (tsy@math08.math.ac.cn)
Lansun Chen
Affiliation:
Institute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, P. R. China. (tsy@math08.math.ac.cn)
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Abstract

We analyze a two species discrete predator-prey model inwhich the prey disperses between two patches of a heterogeneous environmentwith barriers and the mature predator disperses between thepatches with no barrier. By using the discrete dynamical system generated by a monotone, concavemaps for subcommunity of prey, we obtain the subcommunity of preyexists an equilibrium which attracts all positive solutions, andusing the stability trichotomy results on the monotone andcontinuous operator, we obtain some sufficient conditions for thepermanence of species. These results are applied to the modelswith rational growth functions and exponential growth functions.We also present numerical examples to illustrate the dynamiccomplexity of systems.

Keywords

Age-structurenatural barriersubcommunitypersistence.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 35 , Issue 4 , July 2001 , pp. 675 - 690
Copyright
© EDP Sciences, SMAI, 2001

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