Globally Attractive of a Ratio-Dependent Lotka-Volterra Predator-Prey Model with Feedback Control

Changyou Wang; Hao Liu; Shuang Pan; Xiaolin Su; Rui Li

doi:doi:10.11648/j.abb.20160405.13

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Globally Attractive of a Ratio-Dependent Lotka-Volterra Predator-Prey Model with Feedback Control

Changyou Wang, Hao Liu, Shuang Pan, Xiaolin Su, Rui Li

Published in Advances in Bioscience and Bioengineering (Volume 4, Issue 5)

Received: 15 September 2016 Accepted: 27 September 2016 Published: 19 October 2016

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Abstract

By constructing suitable Lyapunov function and developing some new analysis techniques, a Lotka-Volterra predator-prey system with ratio-dependent functional responses and feedback controls is studied and a sufficient condition which guarantees the globally attractive of positive solution for the predator-prey model is obtained. Moreover, the numerical simulation to the system is given to illustrate our results.

Published in	Advances in Bioscience and Bioengineering (Volume 4, Issue 5)
DOI	10.11648/j.abb.20160405.13
Page(s)	59-66
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), 2016. Published by Science Publishing Group

Keywords

Predator-Prey System, Feedback Control, Ratio-Dependent, Globally Attractive

References

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[3]	L. Nie, Z. Teng, L. Hu, J. Peng, Permanence and stability in non-autonomous predator-prey Lotka-Volterra systems with feedback controls, Computers & Mathematics with Applications 58 (2009) 436-448.
[4]	Y. Li, T. Zhang, Permanence of a discrete n-species cooperation system with time-varying delays and feedback controls, Mathematical and Computer Modelling 53 (2011) 1320-1330.
[5]	Y. Fan, L. Wang, Global asymptotical stability of a Logistic model with feedback control, Nonlinear Anal. Real World Applications 11 (2010) 2686-2697.
[6]	K. Gopalsamy, P. Weng, Global attractivity in a competition system with feedback controls, Computers & Mathematics with Applications 45 (2003) 665-676.
[7]	F. Chen, The permanence and global attractivity of Lotka–Volterra competition system with feedback controls, Nonlinear Anal: Real World Applications 7 (2006) 133-143.
[8]	J. Li, A. Zhao, J. Yan, The permanence and global attractivity of a Kolmogorov system with feedback controls, Nonlinear Anal. Real World Applications 10 (2009) 506-518.
[9]	Z. Yang, Positive periodic solutions of a class of single species neutral models with state dependent delay and feedback control, European Journal of Applied Mathematics 17 (2006) 735-757.
[10]	B. Liu, Z. Teng, L. Chen, Analysis of a predator-prey model with Holling II functional response concerning impulsive control strategy, Journal of Computational and Applied Mathematics 193 (2006) 347-362.
[11]	Y. Lv, R. Yuan, Y. Pei, Two types of predator-prey models with harvesting: non-smooth and non-continuous, J. Comput. Appl. Math. 250 (2013)122-142.
[12]	Y. Li, D. Xie, J. Cui, Complex dynamics of a predator-prey model with impulsive state feedback control, Applied Mathematics and Computation 230 (2014) 395-405.
[13]	T. Zhang, W. Ma, X. Meng, T. Zhang, Periodic solution of a prey-predator model with nonlinear state feedback control, Applied Mathematics and Computation 266 (2015) 95–107.
[14]	Jin Yang, Sanyi Tang, Holling type II predator-prey model with nonlinear pulse as state-dependent feedback control, Journal of Computational and Applied Mathematics 291 (2016)225-241.
[15]	C. Y. Wang, X. W. Li, H. Yuan, The permanence of a ratio-dependent Lotka-Volterra predator-prey model with feedback control, Advanced Materials Research 765-767 (2013) 2144-2147.
[16]	J. Wang, K. Wang, Dynamics of a ratio-dependent one predator-two competing prey model, Mathematica Applicata 17 (2004) 172-178. (In Chinese).
[17]	H. K. Khalil, Nonlinear Systems, 3rd ed. Englewood Cliffs: Prentice-Hall, 2002.

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APA Style

Changyou Wang, Hao Liu, Shuang Pan, Xiaolin Su, Rui Li. (2016). Globally Attractive of a Ratio-Dependent Lotka-Volterra Predator-Prey Model with Feedback Control. Advances in Bioscience and Bioengineering, 4(5), 59-66. https://doi.org/10.11648/j.abb.20160405.13

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ACS Style

Changyou Wang; Hao Liu; Shuang Pan; Xiaolin Su; Rui Li. Globally Attractive of a Ratio-Dependent Lotka-Volterra Predator-Prey Model with Feedback Control. Adv. BioSci. Bioeng. 2016, 4(5), 59-66. doi: 10.11648/j.abb.20160405.13

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AMA Style

Changyou Wang, Hao Liu, Shuang Pan, Xiaolin Su, Rui Li. Globally Attractive of a Ratio-Dependent Lotka-Volterra Predator-Prey Model with Feedback Control. Adv BioSci Bioeng. 2016;4(5):59-66. doi: 10.11648/j.abb.20160405.13

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@article{10.11648/j.abb.20160405.13,
  author = {Changyou Wang and Hao Liu and Shuang Pan and Xiaolin Su and Rui Li},
  title = {Globally Attractive of a Ratio-Dependent Lotka-Volterra Predator-Prey Model with Feedback Control},
  journal = {Advances in Bioscience and Bioengineering},
  volume = {4},
  number = {5},
  pages = {59-66},
  doi = {10.11648/j.abb.20160405.13},
  url = {https://doi.org/10.11648/j.abb.20160405.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.abb.20160405.13},
  abstract = {By constructing suitable Lyapunov function and developing some new analysis techniques, a Lotka-Volterra predator-prey system with ratio-dependent functional responses and feedback controls is studied and a sufficient condition which guarantees the globally attractive of positive solution for the predator-prey model is obtained. Moreover, the numerical simulation to the system is given to illustrate our results.},
 year = {2016}
}

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TY  - JOUR
T1  - Globally Attractive of a Ratio-Dependent Lotka-Volterra Predator-Prey Model with Feedback Control
AU  - Changyou Wang
AU  - Hao Liu
AU  - Shuang Pan
AU  - Xiaolin Su
AU  - Rui Li
Y1  - 2016/10/19
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DO  - 10.11648/j.abb.20160405.13
T2  - Advances in Bioscience and Bioengineering
JF  - Advances in Bioscience and Bioengineering
JO  - Advances in Bioscience and Bioengineering
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PB  - Science Publishing Group
SN  - 2330-4162
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AB  - By constructing suitable Lyapunov function and developing some new analysis techniques, a Lotka-Volterra predator-prey system with ratio-dependent functional responses and feedback controls is studied and a sufficient condition which guarantees the globally attractive of positive solution for the predator-prey model is obtained. Moreover, the numerical simulation to the system is given to illustrate our results.
VL  - 4
IS  - 5
ER  -

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Author Information

Changyou Wang

Key Laboratory of Industrial Internet of Things & Networked Control of Ministry of Education, Chongqing University of Posts and Telecommunications, Chongqing, P.R. China
Hao Liu

Key Laboratory of Industrial Internet of Things & Networked Control of Ministry of Education, Chongqing University of Posts and Telecommunications, Chongqing, P.R. China
Shuang Pan

Key Laboratory of Industrial Internet of Things & Networked Control of Ministry of Education, Chongqing University of Posts and Telecommunications, Chongqing, P.R. China
Xiaolin Su

College of Science, Chongqing University of Posts and Telecommunications, Chongqing, P. R. China
Rui Li

Key Laboratory of Industrial Internet of Things & Networked Control of Ministry of Education, Chongqing University of Posts and Telecommunications, Chongqing, P.R. China

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Plain Text BibTeX RIS

APA Style

Changyou Wang, Hao Liu, Shuang Pan, Xiaolin Su, Rui Li. (2016). Globally Attractive of a Ratio-Dependent Lotka-Volterra Predator-Prey Model with Feedback Control. Advances in Bioscience and Bioengineering, 4(5), 59-66. https://doi.org/10.11648/j.abb.20160405.13

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ACS Style

Changyou Wang; Hao Liu; Shuang Pan; Xiaolin Su; Rui Li. Globally Attractive of a Ratio-Dependent Lotka-Volterra Predator-Prey Model with Feedback Control. Adv. BioSci. Bioeng. 2016, 4(5), 59-66. doi: 10.11648/j.abb.20160405.13

Copy | Download

AMA Style

Changyou Wang, Hao Liu, Shuang Pan, Xiaolin Su, Rui Li. Globally Attractive of a Ratio-Dependent Lotka-Volterra Predator-Prey Model with Feedback Control. Adv BioSci Bioeng. 2016;4(5):59-66. doi: 10.11648/j.abb.20160405.13

Copy | Download

@article{10.11648/j.abb.20160405.13,
  author = {Changyou Wang and Hao Liu and Shuang Pan and Xiaolin Su and Rui Li},
  title = {Globally Attractive of a Ratio-Dependent Lotka-Volterra Predator-Prey Model with Feedback Control},
  journal = {Advances in Bioscience and Bioengineering},
  volume = {4},
  number = {5},
  pages = {59-66},
  doi = {10.11648/j.abb.20160405.13},
  url = {https://doi.org/10.11648/j.abb.20160405.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.abb.20160405.13},
  abstract = {By constructing suitable Lyapunov function and developing some new analysis techniques, a Lotka-Volterra predator-prey system with ratio-dependent functional responses and feedback controls is studied and a sufficient condition which guarantees the globally attractive of positive solution for the predator-prey model is obtained. Moreover, the numerical simulation to the system is given to illustrate our results.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Globally Attractive of a Ratio-Dependent Lotka-Volterra Predator-Prey Model with Feedback Control
AU  - Changyou Wang
AU  - Hao Liu
AU  - Shuang Pan
AU  - Xiaolin Su
AU  - Rui Li
Y1  - 2016/10/19
PY  - 2016
N1  - https://doi.org/10.11648/j.abb.20160405.13
DO  - 10.11648/j.abb.20160405.13
T2  - Advances in Bioscience and Bioengineering
JF  - Advances in Bioscience and Bioengineering
JO  - Advances in Bioscience and Bioengineering
SP  - 59
EP  - 66
PB  - Science Publishing Group
SN  - 2330-4162
UR  - https://doi.org/10.11648/j.abb.20160405.13
AB  - By constructing suitable Lyapunov function and developing some new analysis techniques, a Lotka-Volterra predator-prey system with ratio-dependent functional responses and feedback controls is studied and a sufficient condition which guarantees the globally attractive of positive solution for the predator-prey model is obtained. Moreover, the numerical simulation to the system is given to illustrate our results.
VL  - 4
IS  - 5
ER  -

Copy | Download