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.
Mots clés : age-structure, natural barrier, subcommunity, persistence
@article{M2AN_2001__35_4_675_0, author = {Tang, Sanyi and Chen, Lansun}, title = {A discrete predator-prey system with age-structure for predator and natural barriers for prey}, journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique}, pages = {675--690}, publisher = {EDP-Sciences}, volume = {35}, number = {4}, year = {2001}, mrnumber = {1862874}, zbl = {0993.39009}, language = {en}, url = {http://www.numdam.org/item/M2AN_2001__35_4_675_0/} }
TY - JOUR AU - Tang, Sanyi AU - Chen, Lansun TI - A discrete predator-prey system with age-structure for predator and natural barriers for prey JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2001 SP - 675 EP - 690 VL - 35 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/item/M2AN_2001__35_4_675_0/ LA - en ID - M2AN_2001__35_4_675_0 ER -
%0 Journal Article %A Tang, Sanyi %A Chen, Lansun %T A discrete predator-prey system with age-structure for predator and natural barriers for prey %J ESAIM: Modélisation mathématique et analyse numérique %D 2001 %P 675-690 %V 35 %N 4 %I EDP-Sciences %U http://www.numdam.org/item/M2AN_2001__35_4_675_0/ %G en %F M2AN_2001__35_4_675_0
Tang, Sanyi; Chen, Lansun. A discrete predator-prey system with age-structure for predator and natural barriers for prey. ESAIM: Modélisation mathématique et analyse numérique, Tome 35 (2001) no. 4, pp. 675-690. http://www.numdam.org/item/M2AN_2001__35_4_675_0/
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