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

Sanyi Tang; Lansun Chen

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

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

Abstract

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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.

How to cite

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Tang, 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 35.4 (2010): 675-690. <http://eudml.org/doc/197492>.

@article{Tang2010,
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},
keywords = {Age-structure; natural barrier; subcommunity; persistence.; discrete predator-prey model; persistence; age-structure; discrete dynamic system; stability trichotomy},
language = {eng},
month = {3},
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/197492},
volume = {35},
year = {2010},
}

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
DA - 2010/3//
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; persistence; age-structure; discrete dynamic system; stability trichotomy
UR - http://eudml.org/doc/197492
ER -

References

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