Search Advanced

Mathematical Biosciences and Engineering

2014, Volume 11, Issue 2: 167-188. doi: 10.3934/mbe.2014.11.167
Previous Article Next Article

A non-autonomous stochastic predator-prey model

  • 1.
    Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università di Napoli Federico II, Via Cintia, 80126 Napoli
  • 2.
    Dipartimento di Studi e Ricerche Aziendali, (Management & Information Technology), Università di Salerno, Via Ponte don Melillo, 84084 Fisciano (SA)
  • Received: 01 September 2012 Accepted: 29 June 2018 Published: 01 October 2013

  • MSC : Primary: 92D25, 60J60; Secondary: 60K37.

  • The aim of this paper is to consider a non-autonomous predator-prey-like system, with a Gompertz growth law for the prey.By introducing random variations in both prey birth and predator death rates,a stochastic model for the predator-prey-like system in a random environment is proposed and investigated.The corresponding Fokker-Planck equation is solved to obtain the joint probability density for the prey and predator populations and the marginal probability densities.The asymptotic behavior of the predator-prey stochastic model is also analyzed.

    Citation: Aniello Buonocore, Luigia Caputo, Enrica Pirozzi, Amelia G. Nobile. A non-autonomous stochastic predator-prey model[J]. Mathematical Biosciences and Engineering, 2014, 11(2): 167-188. doi: 10.3934/mbe.2014.11.167

    Related Papers:

  • The aim of this paper is to consider a non-autonomous predator-prey-like system, with a Gompertz growth law for the prey.By introducing random variations in both prey birth and predator death rates,a stochastic model for the predator-prey-like system in a random environment is proposed and investigated.The corresponding Fokker-Planck equation is solved to obtain the joint probability density for the prey and predator populations and the marginal probability densities.The asymptotic behavior of the predator-prey stochastic model is also analyzed.


    加载中
    [1] Phys Rev. E, 70, 041910 (2004) 1-7.
    [2] Ecological Complexity, 4 (2007), 242-249.
    [3] Theor. Pop. Biol., 5 (1974), 28-41.
    [4] Kybernetik, 15 (1974), 147-157.
    [5] Phys Rev. E, 65, 036204 (2002), 1-7.
    [6] Proceedings of the Royal Society of Edinburgh, 133A (2003), 97-118.
    [7] Theor. Popul. Biol., 7 (1975), 197-207.
    [8] Reviews of Modern Physics, 43, Part 1 (1971), 231-276.
    [9] Dover Publications, Inc., New York, 1958.
    [10] J. Math. Biol., 36 (1998), 389-406.
    [11] Princeton University Press, Princeton, 1973.
    [12] Oxford University Press, 1976.
    [13] in Some Mathematical Questions in Biology. III., Lectures on Mathematics in the Life Sciences, 4, The American Mathematical Society, Providence, Rhode Island, (1972), 101-143.
    [14] Biol. Cybern., 49 (1984), 179-188.
    [15] Biol. Cybern., 50 (1984), 285-299.
    [16] Interdisciplinary Applied Mathematics, 14, Mathematical Biology, Springer, 2001.
    [17] Lecture Notes in Biomathematics, 14, Berlin, Heidelberg, New York, Springer, 1977.
    [18] in Mathematical Ecology (eds. T. G. Hallam and S. A. Levin), (Miramare Trieste, 1982), Biomathematics, 17, Springer Verlag, Berlin, (1986), 191-238.
    [19] Irish Math. Soc. Bulletin, 48 (2002), 57-63.
    [20] Les Grands Classiques Gauthier-Villars, Paris, 1931.
    [21] Rev. Modern Phys., 17 (1945), 323-342.
    [22] Applied Mathematics and Computation, 218 (2011), 3100-3109.
    [23] International Mathematical Forum, 5 (2010), 3309-3322.
    [24] Chin. Phys. Lett., 23 (2006), 742-745.
  • Reader Comments
  • © 2014 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
Mathematical Biosciences and Engineering
3.9

Metrics

Article views(2390) PDF downloads(508) Cited by(5)

Preview PDF
Download XML
Export Citation
Article outline

Other Articles By Authors

Related pages

Tools

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog