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Stability in the mean of a stochastic three species food chain model with general Le´vy jumps

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  • Zeng, Ting
  • Teng, Zhidong
  • Li, Zhiming
  • Hu, Junna

Abstract

A stochastic three species food chain model with general Le´vy jumps is investigated in the paper. The criterion on the global stability in the mean with probability one for each species is established. The results show that the dynamics of the model can be significantly changed by Le´vy jumps, and strongly indicate that the general jump N(dt, du) is more complicated than compensated jump N˜(dt,du).

Suggested Citation

  • Zeng, Ting & Teng, Zhidong & Li, Zhiming & Hu, Junna, 2018. "Stability in the mean of a stochastic three species food chain model with general Le´vy jumps," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 258-265.
    • Handle: RePEc:eee:chsofr:v:106:y:2018:i:c:p:258-265
    DOI: 10.1016/j.chaos.2017.10.025
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    References listed on IDEAS

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    1. Yu, Jingyi & Liu, Meng, 2017. "Stationary distribution and ergodicity of a stochastic food-chain model with Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 482(C), pages 14-28.
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    3. Zhou, Yanli & Yuan, Sanling & Zhao, Dianli, 2016. "Threshold behavior of a stochastic SIS model with Le´vy jumps," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 255-267.
    4. Liu, Meng & Bai, Chuanzhi, 2016. "Dynamics of a stochastic one-prey two-predator model with Lévy jumps," Applied Mathematics and Computation, Elsevier, vol. 284(C), pages 308-321.
    5. 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:

    1. Mingjing Du & Junmei Li & Yulan Wang & Wei Zhang, 2019. "Numerical Simulation of a Class of Three-Dimensional Kolmogorov Model with Chaotic Dynamic Behavior by Using Barycentric Interpolation Collocation Method," Complexity, Hindawi, vol. 2019, pages 1-14, April.
    2. Rihan, F.A. & Rajivganthi, C, 2020. "Dynamics of fractional-order delay differential model of prey-predator system with Holling-type III and infection among predators," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    3. Alsakaji, Hebatallah J. & Kundu, Soumen & Rihan, Fathalla A., 2021. "Delay differential model of one-predator two-prey system with Monod-Haldane and holling type II functional responses," Applied Mathematics and Computation, Elsevier, vol. 397(C).

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