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

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- 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 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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