Mathematical Biosciences and Engineering, 2014, 11(2): 167-188. doi: 10.3934/mbe.2014.11.167.

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

Export file:

Format

  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text

Content

  • Citation Only
  • Citation and Abstract

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)

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.
  Figure/Table
  Supplementary
  Article Metrics

Keywords Predator-prey system; probability densities; asymptotic behavior.; stochastic model

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

References

  • 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.

 

This article has been cited by

  • 1. Patricia Román-Román, Juan Serrano-Pérez, Francisco Torres-Ruiz, Some Notes about Inference for the Lognormal Diffusion Process with Exogenous Factors, Mathematics, 2018, 6, 5, 85, 10.3390/math6050085

Reader Comments

your name: *   your email: *  

Copyright Info: 2014, Aniello Buonocore, et al., licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved