Permanence of a Lotka-Volterra Predator-Prey Model with Feedback Controls and Prey Diffusion

Shuang Pan; Yonghong Li; Changyou Wang

doi:doi:10.11648/j.ml.20180401.12

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Permanence of a Lotka-Volterra Predator-Prey Model with Feedback Controls and Prey Diffusion

Shuang Pan, Yonghong Li, Changyou Wang

Published in Mathematics Letters (Volume 4, Issue 1)

Received: 19 January 2018 Accepted: 6 February 2018 Published: 28 February 2018

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Abstract

This paper is concerned with a multi-delay three-species predator-prey model with feedback controls and prey diffusion. By developing some new analysis techniques and using the comparison principle of differential equations, we obtained some new sufficient conditions which ensure the system to be permanent.

Published in	Mathematics Letters (Volume 4, Issue 1)
DOI	10.11648/j.ml.20180401.12
Page(s)	6-13
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), 2018. Published by Science Publishing Group

Keywords

Predator-Prey Model, Feedback Control, Time Delay, Diffusion, Permanence

References

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[4]	CHEN F, XIE X. Permanence and Extinction in Nonlinear Single and Multiple Species System with Diffusion. Applied Mathematics and Computation, 2006, 177 (1): 410-426.
[5]	ZHANG F, ZHAO X. Global Dynamics of a Nonautonomous Predator-Prey System with Dispersion. Mathematical Analysis, 2007, 14 (1): 81-87.
[6]	WEI F, LIN Y, QUE L, et al. Periodic Solution and Global Stability for a Nonautonomous Competitive Lotka–Volterra Diffusion System. Applied Mathematics and Computation, 2010, 216 (10): 3097-3104.
[7]	MUHAMMADHAJI A, TENG Z, REHIM M. Dynamical Behavior for a Class of Delayed Competitive-Mutulism Systems. Differential Equations and Dynamical Systems, 2015, 23 (3): 281-301.
[8]	XU R, CHAPLAIN M, DAVIDSON F A. Periodic Solution of a Lotka–Volterra Predator–Prey Model with Dispersion and Time Delays. Applied Mathematics and Computation, 2004, 148 (2): 537-560.
[9]	ZHOU X, SHI X, SONG X. Analysis of Nonautonomous Predator-Prey Model with Nonlinear Diffusion and Time Delay. Applied Mathematics and Computation, 2008, 196(1): 129-136.
[10]	ZHANG Z, WANG Z. Periodic Solutions of a Two-Species Ratio-Dependent Predator-Prey System With TimeDelay in a Two-Patch Environment. Anziam Journal, 2003, 45 (2): 233-244.
[11]	LIANG R, SHEN J. Positive Periodic Solutions for Impulsive Predator–Prey Model with Dispersion and Time Delays. Applied Mathematics and Computation, 2010, 217 (2): 661-676.
[12]	MUHAMMADHAJI A, MAHEMUTI R, TENG Z. On a Periodic Predator-Prey System with Nonlinear Diffusion and Delays. Afrika Matematika, 2016, 27 (7-8): 1179-1197.
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[14]	CHEN F. The Permanence and Global Attractivity of Lotka–Volterra Competition System with Feedback Controls. Nonlinear Analysis: Real World Applications, 2006, 7 (1): 133-143.
[15]	NIE L, TENGA Z, HU L, et al. Permanence and Stability in Nonautonomous Predator–Prey Lotka–Volterra Systems with Feedback Controls. Computers and Mathematics with Applications, 2009, 58 (3): 436-448.
[16]	CHEN F, GONG X, PU L, et al. Dynamic Behaviors of a Lotka-Volterra Predator-Prey System with Feedback Controls. Journal of Biomathematics, 2015, 30 (2): 328-332. (In chinese).
[17]	DING X, FANGFANGWANG. Positive Periodic Solution for a Semi-Ratio-Dependent Predator–Prey System with Diffusion and Time Delays. Nonlinear Analysis: RealWorld Applications, 2008, 9 (2): 239-249.
[18]	GOPALSAMY K, WENG P. Feedback Regulation of Logistic Growth. International Journal of Mathematics & Mathematical Sciences, 1993, 16 (1): 177-192.
[19]	XU J, CHEN F. Permanence of a Lotka-Volterra Cooperative System with Time Delays and Feedback Controls. Communications in Mathematical Biology & Neuroscience, 2015, 18. (2): 226-237.
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APA Style

Shuang Pan, Yonghong Li, Changyou Wang. (2018). Permanence of a Lotka-Volterra Predator-Prey Model with Feedback Controls and Prey Diffusion. Mathematics Letters, 4(1), 6-13. https://doi.org/10.11648/j.ml.20180401.12

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ACS Style

Shuang Pan; Yonghong Li; Changyou Wang. Permanence of a Lotka-Volterra Predator-Prey Model with Feedback Controls and Prey Diffusion. Math. Lett. 2018, 4(1), 6-13. doi: 10.11648/j.ml.20180401.12

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AMA Style

Shuang Pan, Yonghong Li, Changyou Wang. Permanence of a Lotka-Volterra Predator-Prey Model with Feedback Controls and Prey Diffusion. Math Lett. 2018;4(1):6-13. doi: 10.11648/j.ml.20180401.12

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@article{10.11648/j.ml.20180401.12,
  author = {Shuang Pan and Yonghong Li and Changyou Wang},
  title = {Permanence of a Lotka-Volterra Predator-Prey Model with Feedback Controls and Prey Diffusion},
  journal = {Mathematics Letters},
  volume = {4},
  number = {1},
  pages = {6-13},
  doi = {10.11648/j.ml.20180401.12},
  url = {https://doi.org/10.11648/j.ml.20180401.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ml.20180401.12},
  abstract = {This paper is concerned with a multi-delay three-species predator-prey model with feedback controls and prey diffusion. By developing some new analysis techniques and using the comparison principle of differential equations, we obtained some new sufficient conditions which ensure the system to be permanent.},
 year = {2018}
}

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TY  - JOUR
T1  - Permanence of a Lotka-Volterra Predator-Prey Model with Feedback Controls and Prey Diffusion
AU  - Shuang Pan
AU  - Yonghong Li
AU  - Changyou Wang
Y1  - 2018/02/28
PY  - 2018
N1  - https://doi.org/10.11648/j.ml.20180401.12
DO  - 10.11648/j.ml.20180401.12
T2  - Mathematics Letters
JF  - Mathematics Letters
JO  - Mathematics Letters
SP  - 6
EP  - 13
PB  - Science Publishing Group
SN  - 2575-5056
UR  - https://doi.org/10.11648/j.ml.20180401.12
AB  - This paper is concerned with a multi-delay three-species predator-prey model with feedback controls and prey diffusion. By developing some new analysis techniques and using the comparison principle of differential equations, we obtained some new sufficient conditions which ensure the system to be permanent.
VL  - 4
IS  - 1
ER  -

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Author Information

Shuang Pan

College of Automation, Chongqing University of Posts and Telecommunications, Chongqing, P. R. China
Yonghong Li

Institute of Applied Mathematics, Chongqing University of Posts and Telecommunications, Chongqing, P. R. China
Changyou Wang

Institute of Applied Mathematics, Chongqing University of Posts and Telecommunications, Chongqing, P. R. China

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APA Style

Shuang Pan, Yonghong Li, Changyou Wang. (2018). Permanence of a Lotka-Volterra Predator-Prey Model with Feedback Controls and Prey Diffusion. Mathematics Letters, 4(1), 6-13. https://doi.org/10.11648/j.ml.20180401.12

Copy | Download

ACS Style

Shuang Pan; Yonghong Li; Changyou Wang. Permanence of a Lotka-Volterra Predator-Prey Model with Feedback Controls and Prey Diffusion. Math. Lett. 2018, 4(1), 6-13. doi: 10.11648/j.ml.20180401.12

Copy | Download

AMA Style

Shuang Pan, Yonghong Li, Changyou Wang. Permanence of a Lotka-Volterra Predator-Prey Model with Feedback Controls and Prey Diffusion. Math Lett. 2018;4(1):6-13. doi: 10.11648/j.ml.20180401.12

Copy | Download

@article{10.11648/j.ml.20180401.12,
  author = {Shuang Pan and Yonghong Li and Changyou Wang},
  title = {Permanence of a Lotka-Volterra Predator-Prey Model with Feedback Controls and Prey Diffusion},
  journal = {Mathematics Letters},
  volume = {4},
  number = {1},
  pages = {6-13},
  doi = {10.11648/j.ml.20180401.12},
  url = {https://doi.org/10.11648/j.ml.20180401.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ml.20180401.12},
  abstract = {This paper is concerned with a multi-delay three-species predator-prey model with feedback controls and prey diffusion. By developing some new analysis techniques and using the comparison principle of differential equations, we obtained some new sufficient conditions which ensure the system to be permanent.},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - Permanence of a Lotka-Volterra Predator-Prey Model with Feedback Controls and Prey Diffusion
AU  - Shuang Pan
AU  - Yonghong Li
AU  - Changyou Wang
Y1  - 2018/02/28
PY  - 2018
N1  - https://doi.org/10.11648/j.ml.20180401.12
DO  - 10.11648/j.ml.20180401.12
T2  - Mathematics Letters
JF  - Mathematics Letters
JO  - Mathematics Letters
SP  - 6
EP  - 13
PB  - Science Publishing Group
SN  - 2575-5056
UR  - https://doi.org/10.11648/j.ml.20180401.12
AB  - This paper is concerned with a multi-delay three-species predator-prey model with feedback controls and prey diffusion. By developing some new analysis techniques and using the comparison principle of differential equations, we obtained some new sufficient conditions which ensure the system to be permanent.
VL  - 4
IS  - 1
ER  -

Copy | Download