Numerical Method of a Class of Stochastic Delay Population Models

Changyou Wang; Kaixiang Yang; Xingcheng Pu; Rui Li

doi:doi:10.11648/j.cse.20180201.13

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Numerical Method of a Class of Stochastic Delay Population Models

Changyou Wang, Kaixiang Yang, Xingcheng Pu, Rui Li

Published in Control Science and Engineering (Volume 2, Issue 1)

Received: 1 December 2018 Accepted: 19 December 2018 Published: 14 January 2019

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Abstract

Our aim in this paper is to present the design and implementation of a new numerical method to solve a class of stochastic delay population models. Firstly, a stochastic predator-prey model with time-delay and white noise is established. And then, a numerical simulation method based on the Milstein method is proposed to simulate the stochastic population model. Finally, the numerical solutions of the population model are obtained by using MATLAB software. The simulation results show that the new numerical simulation method can truly reflect the persistence and extinction process of stochastic predator-prey model, and provide a reference for solving the numerical simulation of the similar population models.

Published in	Control Science and Engineering (Volume 2, Issue 1)
DOI	10.11648/j.cse.20180201.13
Page(s)	27-35
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), 2019. Published by Science Publishing Group

Keywords

Time-Delay, White Noise, Stochastic Population Model, Numerical Simulation

References

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[2]	M. Jovanović, M. Vasilova, Dynamics of non-autonomous stochastic Gilpin-Ayala competition model with time-varying delays, Applied Mathematics and Computation, 219 (2013) 6946-6964.
[3]	A. Lahrouz, A. Settati, Necessary and sufficient condition and persistence of SIRS system with random perturbation, Applied Mathematics and Computation, 233 (2014) 10-19.
[4]	S. Zhang, Random predator-prey system with time delay and diffusion (in Chinese), Acta Matematica Scientia, 35A (2015) 592-603.
[5]	S. Zhang, X. Meng, T. Feng, T. Zhang, Dynamics analysis and numerical simulations of a stochastic non-autonomous predator-prey system with impulsive effects, Nonlinear Analysis: Hybrid Systems, 26 (2017) 19-37.
[6]	M. Liu, K. Wang, Persistence and extinction of a stochastic single-specie model under regime switching in a polluted environment, Journal of theoretical biology, 264 (2010) 934-944.
[7]	M. Liu, K. Wang, Global stability of a nonlinear stochastic predator-prey system with Beddington- DeAngefis functional response, Communications in Nonlinear Science and Numerical Simulation, 16 (2011) 1114-1121.
[8]	M. Liu, K. Wang, Q. Wu, Survival analysis of stochastic competitive models in a polluted environment and stochastic competitive exclusion principle, Bulletin of Mathematical Biology, 73 (2011) 1969-2012.
[9]	Y. Wang, Population dynamical behavior of a stochastic predator-prey system with Beddington-DeAngelis functional response (in Chinese), Harbin Institute of Technology, Harbin, 2011.
[10]	A. Chatterjee, S. Pal, Interspecies competition between prey and two different predators with Holling IV functional response in diffusive system, Computers & Mathematics with Applications, 71(2) (2016) 615-632.
[11]	S. Li, J. Wu, Qualitative Analysis of a Predator-Prey Model with Predator Saturation and Competition, Acta Applicandae Mathematicae, 141(1) (2016) 165-185.
[12]	S. Kundu, S. Maitra, Dynamical behaviour of a delayed three species predator–prey model with cooperation among the prey species, Nonlinear Dynamics, 92 (2) (2018) 627-643.
[13]	C. Wang, H. Liu, S. Pan, X. Su, R. Li, Globally Attractive of a Ratio-Dependent Lotka-Volterra Predator-Prey Model with Feedback Control, Advances in Bioscience and Bioengineering, 4(5) (2016) 59-66.
[14]	C. Wang, Y. Zhou, Y. Li, R. Li, Well-posedness of a ratio-dependent Lotka-Volterra system with feedback control, Boundary Value Problems, 2018, 2018: ID: 117.
[15]	C. Wang, L. Li, Y. Zhou, R. Li, On a delay ratio-dependent predator-prey system with feedback controls and shelter for the prey, International Journal of Biomathematics, 11(7) (2018) ID:1850095.
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APA Style

Changyou Wang, Kaixiang Yang, Xingcheng Pu, Rui Li. (2019). Numerical Method of a Class of Stochastic Delay Population Models. Control Science and Engineering, 2(1), 27-35. https://doi.org/10.11648/j.cse.20180201.13

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ACS Style

Changyou Wang; Kaixiang Yang; Xingcheng Pu; Rui Li. Numerical Method of a Class of Stochastic Delay Population Models. Control Sci. Eng. 2019, 2(1), 27-35. doi: 10.11648/j.cse.20180201.13

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AMA Style

Changyou Wang, Kaixiang Yang, Xingcheng Pu, Rui Li. Numerical Method of a Class of Stochastic Delay Population Models. Control Sci Eng. 2019;2(1):27-35. doi: 10.11648/j.cse.20180201.13

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@article{10.11648/j.cse.20180201.13,
  author = {Changyou Wang and Kaixiang Yang and Xingcheng Pu and Rui Li},
  title = {Numerical Method of a Class of Stochastic Delay Population Models},
  journal = {Control Science and Engineering},
  volume = {2},
  number = {1},
  pages = {27-35},
  doi = {10.11648/j.cse.20180201.13},
  url = {https://doi.org/10.11648/j.cse.20180201.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.cse.20180201.13},
  abstract = {Our aim in this paper is to present the design and implementation of a new numerical method to solve a class of stochastic delay population models. Firstly, a stochastic predator-prey model with time-delay and white noise is established. And then, a numerical simulation method based on the Milstein method is proposed to simulate the stochastic population model. Finally, the numerical solutions of the population model are obtained by using MATLAB software. The simulation results show that the new numerical simulation method can truly reflect the persistence and extinction process of stochastic predator-prey model, and provide a reference for solving the numerical simulation of the similar population models.},
 year = {2019}
}

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TY  - JOUR
T1  - Numerical Method of a Class of Stochastic Delay Population Models
AU  - Changyou Wang
AU  - Kaixiang Yang
AU  - Xingcheng Pu
AU  - Rui Li
Y1  - 2019/01/14
PY  - 2019
N1  - https://doi.org/10.11648/j.cse.20180201.13
DO  - 10.11648/j.cse.20180201.13
T2  - Control Science and Engineering
JF  - Control Science and Engineering
JO  - Control Science and Engineering
SP  - 27
EP  - 35
PB  - Science Publishing Group
SN  - 2994-7421
UR  - https://doi.org/10.11648/j.cse.20180201.13
AB  - Our aim in this paper is to present the design and implementation of a new numerical method to solve a class of stochastic delay population models. Firstly, a stochastic predator-prey model with time-delay and white noise is established. And then, a numerical simulation method based on the Milstein method is proposed to simulate the stochastic population model. Finally, the numerical solutions of the population model are obtained by using MATLAB software. The simulation results show that the new numerical simulation method can truly reflect the persistence and extinction process of stochastic predator-prey model, and provide a reference for solving the numerical simulation of the similar population models.
VL  - 2
IS  - 1
ER  -

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Author Information

Changyou Wang

College of Automation, Chongqing University of Posts and Telecommunications, Chongqing, P. R. China
Kaixiang Yang

College of Automation, Chongqing University of Posts and Telecommunications, Chongqing, P. R. China
Xingcheng Pu

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

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

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Plain Text BibTeX RIS

APA Style

Changyou Wang, Kaixiang Yang, Xingcheng Pu, Rui Li. (2019). Numerical Method of a Class of Stochastic Delay Population Models. Control Science and Engineering, 2(1), 27-35. https://doi.org/10.11648/j.cse.20180201.13

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ACS Style

Changyou Wang; Kaixiang Yang; Xingcheng Pu; Rui Li. Numerical Method of a Class of Stochastic Delay Population Models. Control Sci. Eng. 2019, 2(1), 27-35. doi: 10.11648/j.cse.20180201.13

Copy | Download

AMA Style

Changyou Wang, Kaixiang Yang, Xingcheng Pu, Rui Li. Numerical Method of a Class of Stochastic Delay Population Models. Control Sci Eng. 2019;2(1):27-35. doi: 10.11648/j.cse.20180201.13

Copy | Download

@article{10.11648/j.cse.20180201.13,
  author = {Changyou Wang and Kaixiang Yang and Xingcheng Pu and Rui Li},
  title = {Numerical Method of a Class of Stochastic Delay Population Models},
  journal = {Control Science and Engineering},
  volume = {2},
  number = {1},
  pages = {27-35},
  doi = {10.11648/j.cse.20180201.13},
  url = {https://doi.org/10.11648/j.cse.20180201.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.cse.20180201.13},
  abstract = {Our aim in this paper is to present the design and implementation of a new numerical method to solve a class of stochastic delay population models. Firstly, a stochastic predator-prey model with time-delay and white noise is established. And then, a numerical simulation method based on the Milstein method is proposed to simulate the stochastic population model. Finally, the numerical solutions of the population model are obtained by using MATLAB software. The simulation results show that the new numerical simulation method can truly reflect the persistence and extinction process of stochastic predator-prey model, and provide a reference for solving the numerical simulation of the similar population models.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - Numerical Method of a Class of Stochastic Delay Population Models
AU  - Changyou Wang
AU  - Kaixiang Yang
AU  - Xingcheng Pu
AU  - Rui Li
Y1  - 2019/01/14
PY  - 2019
N1  - https://doi.org/10.11648/j.cse.20180201.13
DO  - 10.11648/j.cse.20180201.13
T2  - Control Science and Engineering
JF  - Control Science and Engineering
JO  - Control Science and Engineering
SP  - 27
EP  - 35
PB  - Science Publishing Group
SN  - 2994-7421
UR  - https://doi.org/10.11648/j.cse.20180201.13
AB  - Our aim in this paper is to present the design and implementation of a new numerical method to solve a class of stochastic delay population models. Firstly, a stochastic predator-prey model with time-delay and white noise is established. And then, a numerical simulation method based on the Milstein method is proposed to simulate the stochastic population model. Finally, the numerical solutions of the population model are obtained by using MATLAB software. The simulation results show that the new numerical simulation method can truly reflect the persistence and extinction process of stochastic predator-prey model, and provide a reference for solving the numerical simulation of the similar population models.
VL  - 2
IS  - 1
ER  -

Copy | Download