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Dynamics of stochastic delay Lotka–Volterra systems with impulsive toxicant input and Lévy noise in polluted environments

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  • Liu, Qun
  • Chen, Qingmei

Abstract

In this paper, two stochastic delay Lotka–Volterra systems (i.e., competition system and predator–prey system) with impulsive toxicant input and Lévy noise in polluted environments are proposed and investigated. Under some simple assumptions, sufficient and necessary criteria for stability in time average and extinction of each population are established. The thresholds between stability in time average and extinction of each model are obtained. Some recent results are improved and extended greatly.

Suggested Citation

  • Liu, Qun & Chen, Qingmei, 2015. "Dynamics of stochastic delay Lotka–Volterra systems with impulsive toxicant input and Lévy noise in polluted environments," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 52-67.
    • Handle: RePEc:eee:apmaco:v:256:y:2015:i:c:p:52-67
    DOI: 10.1016/j.amc.2015.01.009
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    References listed on IDEAS

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    1. Liu, Meng & Wang, Ke, 2012. "Persistence and extinction of a single-species population system in a polluted environment with random perturbations and impulsive toxicant input," Chaos, Solitons & Fractals, Elsevier, vol. 45(12), pages 1541-1550.
    2. Liu, Meng & Wang, Ke, 2009. "Survival analysis of stochastic single-species population models in polluted environments," Ecological Modelling, Elsevier, vol. 220(9), pages 1347-1357.
    3. Jiao, Jianjun & Ye, Kaili & Chen, Lansun, 2011. "Dynamical analysis of a five-dimensioned chemostat model with impulsive diffusion and pulse input environmental toxicant," Chaos, Solitons & Fractals, Elsevier, vol. 44(1), pages 17-27.
    4. Wan, Li & Zhou, Qinghua, 2009. "Stochastic Lotka-Volterra model with infinite delay," Statistics & Probability Letters, Elsevier, vol. 79(5), pages 698-706, March.
    5. Yang, Xiaofeng & Jin, Zhen & Xue, Yakui, 2007. "Weak average persistence and extinction of a predator–prey system in a polluted environment with impulsive toxicant input," Chaos, Solitons & Fractals, Elsevier, vol. 31(3), pages 726-735.
    6. Peng, Shige & Zhu, Xuehong, 2006. "Necessary and sufficient condition for comparison theorem of 1-dimensional stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 116(3), pages 370-380, March.
    7. Mao, Xuerong & Marion, Glenn & Renshaw, Eric, 2002. "Environmental Brownian noise suppresses explosions in population dynamics," Stochastic Processes and their Applications, Elsevier, vol. 97(1), pages 95-110, January.
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    Cited by:

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    2. Liu, Meng & Bai, Chuanzhi & Deng, Meiling & Du, Bo, 2016. "Analysis of stochastic two-prey one-predator model with Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 445(C), pages 176-188.

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