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Extinction and Persistence in Mean of a Novel Delay Impulsive Stochastic Infected Predator-Prey System with Jumps

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  • Guodong Liu
  • Xiaohong Wang
  • Xinzhu Meng
  • Shujing Gao

Abstract

In this paper, we explore an impulsive stochastic infected predator-prey system with Lévy jumps and delays. The main aim of this paper is to investigate the effects of time delays and impulse stochastic interference on dynamics of the predator-prey model. First, we prove some properties of the subsystem of the system. Second, in view of comparison theorem and limit superior theory, we obtain the sufficient conditions for the extinction of this system. Furthermore, persistence in mean of the system is also investigated by using the theory of impulsive stochastic differential equations (ISDE) and delay differential equations (DDE). Finally, we carry out some simulations to verify our main results and explain the biological implications.

Suggested Citation

  • Guodong Liu & Xiaohong Wang & Xinzhu Meng & Shujing Gao, 2017. "Extinction and Persistence in Mean of a Novel Delay Impulsive Stochastic Infected Predator-Prey System with Jumps," Complexity, Hindawi, vol. 2017, pages 1-15, June.
    • Handle: RePEc:hin:complx:1950970
    DOI: 10.1155/2017/1950970
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    References listed on IDEAS

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    1. Zhao, Dianli & Yuan, Sanling, 2016. "Dynamics of the stochastic Leslie–Gower predator–prey system with randomized intrinsic growth rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 419-428.
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    3. Wencai Zhao & Tongqian Zhang & Zhengbo Chang & Xinzhu Meng & Yulin Liu, 2013. "Dynamical Analysis of SIR Epidemic Models with Distributed Delay," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-15, July.
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    Cited by:

    1. Feifei Bian & Wencai Zhao & Yi Song & Rong Yue, 2017. "Dynamical Analysis of a Class of Prey-Predator Model with Beddington-DeAngelis Functional Response, Stochastic Perturbation, and Impulsive Toxicant Input," Complexity, Hindawi, vol. 2017, pages 1-18, December.
    2. Lv, Xuejin & Meng, Xinzhu & Wang, Xinzeng, 2018. "Extinction and stationary distribution of an impulsive stochastic chemostat model with nonlinear perturbation," Chaos, Solitons & Fractals, Elsevier, vol. 110(C), pages 273-279.
    3. Bor-Sen Chen & Xiangyun Lin & Weihai Zhang & Tianshou Zhou, 2018. "On the System Entropy and Energy Dissipativity of Stochastic Systems and Their Application in Biological Systems," Complexity, Hindawi, vol. 2018, pages 1-18, December.
    4. Yu Mu & Zuxiong Li & Huili Xiang & Hailing Wang, 2019. "Dynamical Analysis of a Stochastic Multispecies Turbidostat Model," Complexity, Hindawi, vol. 2019, pages 1-18, January.
    5. Rong Liu & Guirong Liu, 2018. "Asymptotic Behavior of a Stochastic Two-Species Competition Model under the Effect of Disease," Complexity, Hindawi, vol. 2018, pages 1-15, November.
    6. Yang, Huan & Tan, Yuanshun & Yang, Jin & Liu, Zijian, 2021. "Extinction and persistence of a tumor-immune model with white noise and pulsed comprehensive therapy," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 456-470.
    7. Qi, Haokun & Zhang, Shengqiang & Meng, Xinzhu & Dong, Huanhe, 2018. "Periodic solution and ergodic stationary distribution of two stochastic SIQS epidemic systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 223-241.
    8. Sun, Xinguo & Zuo, Wenjie & Jiang, Daqing & Hayat, Tasawar, 2018. "Unique stationary distribution and ergodicity of a stochastic Logistic model with distributed delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 864-881.
    9. Sun, Shulin & Zhang, Xiaofeng, 2018. "Asymptotic behavior of a stochastic delayed chemostat model with nonmonotone uptake function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 38-56.
    10. Zhenzhen Shi & Yaning Li & Huidong Cheng, 2019. "Dynamic Analysis of a Pest Management Smith Model with Impulsive State Feedback Control and Continuous Delay," Mathematics, MDPI, vol. 7(7), pages 1-15, July.
    11. Gao, Miaomiao & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2019. "Threshold behavior of a stochastic Lotka–Volterra food chain chemostat model with jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 191-203.
    12. Tingting Ma & Xinzhu Meng & Zhengbo Chang, 2019. "Dynamics and Optimal Harvesting Control for a Stochastic One-Predator-Two-Prey Time Delay System with Jumps," Complexity, Hindawi, vol. 2019, pages 1-19, March.
    13. Liu, Fuxiang & Yang, Ruizhi & Tang, Leiyu, 2019. "Hopf bifurcation in a diffusive predator-prey model with competitive interference," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 250-258.
    14. Rengamannar, Kaviya & Balakrishnan, Ganesh Priya & Palanisamy, Muthukumar & Niezabitowski, Michal, 2020. "Exponential stability of non-linear stochastic delay differential system with generalized delay-dependent impulsive points," Applied Mathematics and Computation, Elsevier, vol. 382(C).
    15. Mengnan Chi & Wencai Zhao, 2019. "Dynamical Analysis of Two-Microorganism and Single Nutrient Stochastic Chemostat Model with Monod-Haldane Response Function," Complexity, Hindawi, vol. 2019, pages 1-13, March.

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