A discrete predator-prey system with age-structure for predator and natural barriers for prey
Institute of Mathematics, Academy of Mathematics and System
Sciences, Chinese Academy of Sciences, Beijing 100080, P. R. China. (firstname.lastname@example.org)
Revised: 7 February 2001
We analyze a two species discrete predator-prey model in which the prey disperses between two patches of a heterogeneous environment with barriers and the mature predator disperses between the patches with no barrier. By using the discrete dynamical system generated by a monotone, concave maps for subcommunity of prey, we obtain the subcommunity of prey exists an equilibrium which attracts all positive solutions, and using the stability trichotomy results on the monotone and continuous operator, we obtain some sufficient conditions for the permanence of species. These results are applied to the models with rational growth functions and exponential growth functions. We also present numerical examples to illustrate the dynamic complexity of systems.
Mathematics Subject Classification: 34C35 / 39A10
Key words: Age-structure / natural barrier / subcommunity / persistence.
© EDP Sciences, SMAI, 2001