# A discrete predator-prey system with age-structure for predator and natural barriers for prey

- Volume: 35, Issue: 4, page 675-690
- ISSN: 0764-583X

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topTang, Sanyi, and Chen, Lansun. "A discrete predator-prey system with age-structure for predator and natural barriers for prey." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 35.4 (2001): 675-690. <http://eudml.org/doc/194068>.

@article{Tang2001,

abstract = {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.},

author = {Tang, Sanyi, Chen, Lansun},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {age-structure; natural barrier; subcommunity; persistence; discrete predator-prey model; discrete dynamic system; stability trichotomy},

language = {eng},

number = {4},

pages = {675-690},

publisher = {EDP-Sciences},

title = {A discrete predator-prey system with age-structure for predator and natural barriers for prey},

url = {http://eudml.org/doc/194068},

volume = {35},

year = {2001},

}

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: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2001

PB - EDP-Sciences

VL - 35

IS - 4

SP - 675

EP - 690

AB - 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.

LA - eng

KW - age-structure; natural barrier; subcommunity; persistence; discrete predator-prey model; discrete dynamic system; stability trichotomy

UR - http://eudml.org/doc/194068

ER -

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