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Permanence and extinction of stochastic competitive Lotka–Volterra system with Lévy noise

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Abstract

This paper derives sufficient conditions for stochastic permanence and extinction of a stochastic non-autonomous competitive Lotka–Volterra system with Lévy noise. For the autonomous case, the results show that stochastic permanence and extinction are characterized by two parameters \(\mathcal {B}_{1}\) and \(\mathcal {B}_{2}\): if \(\mathcal {B}_{1}\mathcal {B}_{2} \ne 0\), then the system is either stochastically permanent or extinctive. That is, it is extinctive if and only if \(\mathcal {B}_{1}<0\) and \(\mathcal {B}_{2}<0\); otherwise, it is stochastically permanent. Some existing results are included as special cases. An example and its simulations are given to support our theoretical results.

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Authors and Affiliations

  1. College of Oceanic and Atmospheric Sciences, Ocean University of China, Qingdao, 266071, Shandong, People’s Republic of China

    Tengda Wei

  2. School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, 454003, Henan, People’s Republic of China

    Sheng Wang

  3. School of Mathematics, Ocean University of China, Qingdao, 266071, Shandong, People’s Republic of China

    Linshan Wang

Authors
  1. Tengda Wei
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  2. Sheng Wang
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  3. Linshan Wang
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Corresponding author

Correspondence to Sheng Wang.

Additional information

This work is supported by National Natural Science Foundation of China (No. 11171374).

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Wei, T., Wang, S. & Wang, L. Permanence and extinction of stochastic competitive Lotka–Volterra system with Lévy noise. J. Appl. Math. Comput. 57, 667–683 (2018). https://doi.org/10.1007/s12190-017-1127-y

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  • DOI: https://doi.org/10.1007/s12190-017-1127-y

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