Positive periodic solution for ratio-dependent n -species discrete time system

Mei-Lan Tang; Xin-Ge Liu

Applications of Mathematics (2011)

  • Volume: 56, Issue: 6, page 577-589
  • ISSN: 0862-7940

Abstract

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In this paper, sharp a priori estimate of the periodic solutions is obtained for the discrete analogue of the continuous time ratio-dependent predator-prey system, which is governed by nonautonomous difference equations, modelling the dynamics of the n - 1 competing preys and one predator having nonoverlapping generations. Based on more precise a priori estimate and the continuation theorem of the coincidence degree, an easily verifiable sufficient criterion of the existence of positive periodic solutions is established. The result obtained in this paper greatly improves the existing results.

How to cite

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Tang, Mei-Lan, and Liu, Xin-Ge. "Positive periodic solution for ratio-dependent $n$-species discrete time system." Applications of Mathematics 56.6 (2011): 577-589. <http://eudml.org/doc/196911>.

@article{Tang2011,
abstract = {In this paper, sharp a priori estimate of the periodic solutions is obtained for the discrete analogue of the continuous time ratio-dependent predator-prey system, which is governed by nonautonomous difference equations, modelling the dynamics of the $n-1$ competing preys and one predator having nonoverlapping generations. Based on more precise a priori estimate and the continuation theorem of the coincidence degree, an easily verifiable sufficient criterion of the existence of positive periodic solutions is established. The result obtained in this paper greatly improves the existing results.},
author = {Tang, Mei-Lan, Liu, Xin-Ge},
journal = {Applications of Mathematics},
keywords = {ratio-dependent; predator-prey system; periodic solution; a priori estimate; ratio-dependent; predator-prey system; periodic solution; a priori estimate},
language = {eng},
number = {6},
pages = {577-589},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Positive periodic solution for ratio-dependent $n$-species discrete time system},
url = {http://eudml.org/doc/196911},
volume = {56},
year = {2011},
}

TY - JOUR
AU - Tang, Mei-Lan
AU - Liu, Xin-Ge
TI - Positive periodic solution for ratio-dependent $n$-species discrete time system
JO - Applications of Mathematics
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 56
IS - 6
SP - 577
EP - 589
AB - In this paper, sharp a priori estimate of the periodic solutions is obtained for the discrete analogue of the continuous time ratio-dependent predator-prey system, which is governed by nonautonomous difference equations, modelling the dynamics of the $n-1$ competing preys and one predator having nonoverlapping generations. Based on more precise a priori estimate and the continuation theorem of the coincidence degree, an easily verifiable sufficient criterion of the existence of positive periodic solutions is established. The result obtained in this paper greatly improves the existing results.
LA - eng
KW - ratio-dependent; predator-prey system; periodic solution; a priori estimate; ratio-dependent; predator-prey system; periodic solution; a priori estimate
UR - http://eudml.org/doc/196911
ER -

References

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