Analysis of a stochastic predator–prey population model with Allee effect and jumps View Full Text


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Article Info

DATE

2019-12

AUTHORS

Rong Liu, Guirong Liu

ABSTRACT

This paper is concerned with a stochastic predator–prey model with Allee effect and Lévy noise. First, by the comparison theorem of stochastic differential equations, we prove that the model has a unique global positive solution starting from the positive initial value. Then we investigate the asymptotic pathwise behavior of the model by the generalized exponential martingale inequality and the Borel–Cantelli lemma. Next, we establish the conditions under which predator and prey populations are extinct. Furthermore, we show that the global positive solution is stochastically ultimate bounded under some conditions by using the Bernoulli equation and Chebyshev’s inequality. At last, we introduce some numerical simulations to support the main results obtained. The results in this paper generalize and improve the previous related results. More... »

PAGES

60

References to SciGraph publications

  • 2015-04. Optimal Harvesting of a Stochastic Logistic Model with Time Delay in JOURNAL OF NONLINEAR SCIENCE
  • 2017-12. Stochastic inequalities and applications to dynamics analysis of a novel SIVS epidemic model with jumps in JOURNAL OF INEQUALITIES AND APPLICATIONS
  • 2011-12. Boundedness of positive operators on weighted amalgams in JOURNAL OF INEQUALITIES AND APPLICATIONS
  • 2011-12. Some Weighted Hardy-Type Inequalities on Anisotropic Heisenberg Groups in JOURNAL OF INEQUALITIES AND APPLICATIONS
  • Journal

    TITLE

    Journal of Inequalities and Applications

    ISSUE

    1

    VOLUME

    2019

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1186/s13660-019-2014-x

    DOI

    http://dx.doi.org/10.1186/s13660-019-2014-x

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1112646033


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