Global Asymptotic Stability Analysis of Predator-Prey System

Ahmed Buseri Ashine

doi:doi:10.11648/j.mma.20170204.11

| Peer-Reviewed

Global Asymptotic Stability Analysis of Predator-Prey System

Ahmed Buseri Ashine

Published in Mathematical Modelling and Applications (Volume 2, Issue 4)

Received: 16 May 2017 Accepted: 24 August 2017 Published: 26 September 2017

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

In this paper, a predator-prey model with Holling type II response function is proposed and analyzed. The model is characterized by a couple of system of first order non-linear differential equations. The objective of the work is to offer mathematical analysis of such model. The equilibrium points are computed, boundedness and criteria for stability and persistent of the system are obtained.

Published in	Mathematical Modelling and Applications (Volume 2, Issue 4)
DOI	10.11648/j.mma.20170204.11
Page(s)	40-42
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Prey-Predator, Stability, Persistent, Limit Cycle

References

[1]	Lotka, A.: Elements of Physical Biology. Williams and Wilkins, Baltimore (1925).
[2]	N. Apreutesei, A. Ducrot, V. Volpert, Competition of species with intra-specific competition, Math. Model. Nat. Phenom., 3, pp. 1–27, 2008.
[3]	H. Malchow, S. Petrovskii, E. Venturino, Spatiotemporal Patterns in Ecology and Epidemiology, Chapman & Hall/CRC Press, Boca Raton, 2008.
[4]	Ahmed Buseri Ashine “study on prey-predator model with predator in disease and harvesting” Global Journal of Science Frontier Research 17(2) pp. 23–28.
[5]	S. G. Ruan, D. M. Xiao, Global analysis in a predator-prey system with non-monotonic functional response, SIAM J. Appl. Math., 61, pp. 1445–1472, 2001.
[6]	Berryman AA. The origins and evolutions of predator–prey theory. Ecology 1992;73: 1530–5.
[7]	Kuang Y, Freedman HI. Uniqueness of limit cycles in Gause-type predator–prey systems. Math Biosci 1988;88: 67–84.
[8]	Kuang Y. Nonuniqueness of limit cycles of Gause-type predator–prey systems. Appl Anal 1988;29:269–87.
[9]	Kuang Y. On the location and period of limit cycles in Gause-type predator–prey systems. J Math Anal Appl 1989; 142: 130–43.
[10]	Kuang Y. Limit cycles in a chemo stat-related model. SIAM J Appl Math 1989;49: 1759–67.
[11]	Kuang Y. Global stability of Gauss-type predator–prey systems. J Math Biol 1990;28: 463–74.
[12]	Berreta E, Kuang Y. Convergence results in a well-known delayed predator–prey system. J Math Anal Appl 1996;204: 840–53.
[13]	Birkoff G, Rota GC, Ordinary Differential equations, Ginn; 982.
[14]	Freedman HI. Deterministic mathematical models population ecology. New York: Marcel Dekker; 1980.
[15]	Freedman HI. Waltman P. Persistence in models of three interacting predator-prey population. Math Biosci 1984; 68: 213-31.
[16]	Volterra, V.: Variazionie fluttauazionidel numero dindividui in species animals conviventii. Mem Acd. Linciei 2, 31–33 (1926).

Cite This Article

Plain Text BibTeX RIS

APA Style

Ahmed Buseri Ashine. (2017). Global Asymptotic Stability Analysis of Predator-Prey System. Mathematical Modelling and Applications, 2(4), 40-42. https://doi.org/10.11648/j.mma.20170204.11

Copy | Download

ACS Style

Ahmed Buseri Ashine. Global Asymptotic Stability Analysis of Predator-Prey System. Math. Model. Appl. 2017, 2(4), 40-42. doi: 10.11648/j.mma.20170204.11

Copy | Download

AMA Style

Ahmed Buseri Ashine. Global Asymptotic Stability Analysis of Predator-Prey System. Math Model Appl. 2017;2(4):40-42. doi: 10.11648/j.mma.20170204.11

Copy | Download

@article{10.11648/j.mma.20170204.11,
  author = {Ahmed Buseri Ashine},
  title = {Global Asymptotic Stability Analysis of Predator-Prey System},
  journal = {Mathematical Modelling and Applications},
  volume = {2},
  number = {4},
  pages = {40-42},
  doi = {10.11648/j.mma.20170204.11},
  url = {https://doi.org/10.11648/j.mma.20170204.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mma.20170204.11},
  abstract = {In this paper, a predator-prey model with Holling type II response function is proposed and analyzed. The model is characterized by a couple of system of first order non-linear differential equations. The objective of the work is to offer mathematical analysis of such model. The equilibrium points are computed, boundedness and criteria for stability and persistent of the system are obtained.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Global Asymptotic Stability Analysis of Predator-Prey System
AU  - Ahmed Buseri Ashine
Y1  - 2017/09/26
PY  - 2017
N1  - https://doi.org/10.11648/j.mma.20170204.11
DO  - 10.11648/j.mma.20170204.11
T2  - Mathematical Modelling and Applications
JF  - Mathematical Modelling and Applications
JO  - Mathematical Modelling and Applications
SP  - 40
EP  - 42
PB  - Science Publishing Group
SN  - 2575-1794
UR  - https://doi.org/10.11648/j.mma.20170204.11
AB  - In this paper, a predator-prey model with Holling type II response function is proposed and analyzed. The model is characterized by a couple of system of first order non-linear differential equations. The objective of the work is to offer mathematical analysis of such model. The equilibrium points are computed, boundedness and criteria for stability and persistent of the system are obtained.
VL  - 2
IS  - 4
ER  -

Copy | Download

Author Information

Ahmed Buseri Ashine

Department of Mathematics, Madda Walabu University, Bale Robe, Ethiopia

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Ahmed Buseri Ashine. (2017). Global Asymptotic Stability Analysis of Predator-Prey System. Mathematical Modelling and Applications, 2(4), 40-42. https://doi.org/10.11648/j.mma.20170204.11

Copy | Download

ACS Style

Ahmed Buseri Ashine. Global Asymptotic Stability Analysis of Predator-Prey System. Math. Model. Appl. 2017, 2(4), 40-42. doi: 10.11648/j.mma.20170204.11

Copy | Download

AMA Style

Ahmed Buseri Ashine. Global Asymptotic Stability Analysis of Predator-Prey System. Math Model Appl. 2017;2(4):40-42. doi: 10.11648/j.mma.20170204.11

Copy | Download

@article{10.11648/j.mma.20170204.11,
  author = {Ahmed Buseri Ashine},
  title = {Global Asymptotic Stability Analysis of Predator-Prey System},
  journal = {Mathematical Modelling and Applications},
  volume = {2},
  number = {4},
  pages = {40-42},
  doi = {10.11648/j.mma.20170204.11},
  url = {https://doi.org/10.11648/j.mma.20170204.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mma.20170204.11},
  abstract = {In this paper, a predator-prey model with Holling type II response function is proposed and analyzed. The model is characterized by a couple of system of first order non-linear differential equations. The objective of the work is to offer mathematical analysis of such model. The equilibrium points are computed, boundedness and criteria for stability and persistent of the system are obtained.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Global Asymptotic Stability Analysis of Predator-Prey System
AU  - Ahmed Buseri Ashine
Y1  - 2017/09/26
PY  - 2017
N1  - https://doi.org/10.11648/j.mma.20170204.11
DO  - 10.11648/j.mma.20170204.11
T2  - Mathematical Modelling and Applications
JF  - Mathematical Modelling and Applications
JO  - Mathematical Modelling and Applications
SP  - 40
EP  - 42
PB  - Science Publishing Group
SN  - 2575-1794
UR  - https://doi.org/10.11648/j.mma.20170204.11
AB  - In this paper, a predator-prey model with Holling type II response function is proposed and analyzed. The model is characterized by a couple of system of first order non-linear differential equations. The objective of the work is to offer mathematical analysis of such model. The equilibrium points are computed, boundedness and criteria for stability and persistent of the system are obtained.
VL  - 2
IS  - 4
ER  -

Copy | Download