Skip to main content
SpringerLink
Log in

Analysis of impulsive stochastic delay budworm population model with L\(\acute{\mathrm {e}}\)vy jumps

  • Original Research
  • Published:
Journal of Applied Mathematics and Computing Aims and scope Submit manuscript

Abstract

In this paper, two types impulsive delay stochastic budworm population models are proposed and investigated. Based on some standard assumptions, a series sufficient criteria about long time behavior of the solutions are given. For the unbounded positive impulse, we obtain a sufficient criteria that makes the solution weakly permanent, which is close to the necessary criterion. Then, we demonstrate the conditions that produce the solutions are stochastically permanent when positive impulse is bounded. Finally, numerical simulations of the model confirms our theoretical results. Our rsults improve and extend some previous results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  1. Hallam, T.G., Ma, Z.E.: On density and extinction in continuous population models. J. Biol. Math. 25, 191–201 (1987)

    Article  MATH  Google Scholar 

  2. Hallam, T.G., Clark, C.E., Lassider, R.R.: Effects of toxicants on populations: a qualitative approach I. Equilibrium environmental exposure. Ecol. Model. 18, 291–304 (1983)

    Article  Google Scholar 

  3. Sasmal, S.K., Takeuchi, Y.: Evolutionary dynamics of single species model with Allee effects and aposematism. Nonlinear Anal. Real. 58, 103233 (2021)

    Article  MATH  Google Scholar 

  4. Liu, Z.J., Guo, S.L., Tan, R.H., et al.: Modelling and analysis of a non-autonomous single-species model with impulsive and random perturbations. Appl. Math. Model. 40, 5510–5531 (2016)

    Article  MATH  Google Scholar 

  5. Lv, H.B., Liu, Z.J., Li, Z.X., et al.: Two impulsive stochastic delay single-species models incorporating L\(\acute{\rm e}\)vy noise. J. Appl. Math. Comput. 58, 721–753 (2018)

    Article  Google Scholar 

  6. Xu, Y., Gao, S.J., Chen, D.: Persistence and extinction of a nonautonomous switching single-species population model. Appl. Math. Lett. 103, 106187 (2020)

    Article  MATH  Google Scholar 

  7. Liu, Q., Chen, Q.: Analysis of a general stochastic non-autonomous logistic model with delays and L\(\acute{\rm e}\)vy jumps. J. Math. Anal. Appl. 433, 95–120 (2016)

    Article  Google Scholar 

  8. Gard, T.: Stability for multispecies population models in random environments. Nonlinear Anal. 10, 1411–1419 (1986)

    Article  MATH  Google Scholar 

  9. Gakkhar, S., Singh, A.: Complex dynamics in a prey predator system with multiple delays. Commun. Nonlinear Sci. 17, 914–929 (2012)

    Article  MATH  Google Scholar 

  10. Yang, J.T.: Permanence, extinction and periodic solution of a stochastic single-species model with L\(\acute{\rm e}\)vy noises. Discrete Cont. Dyn-B 26, 5641–5660 (2021)

    MATH  Google Scholar 

  11. Zhang, Y., Lv, J.L., Zhou, X.L.: Dynamics of stochastic single-species models. Math. Meth. Appl. Sci. 43, 8728–8735 (2020)

    Article  MATH  Google Scholar 

  12. Liu, Q., Chen, Q.M.: Analysis of a stochastic delay predator–prey system with jumps in a polluted environment. Appl. Math. Comput. 242, 90–100 (2014)

    MATH  Google Scholar 

  13. Zhao, J.D., Zhang, T.H.: Permanence and extinction of a single species model in polluted environment. Int. J. Biomath. 13, 2500031 (2020)

    Article  Google Scholar 

  14. Deng, Y., Liu, M.: Analysis of stochastic tumor-immune model with regime switching and impulsive perturbations. Appl. Math. Model. 78, 482–504 (2020)

    Article  MATH  Google Scholar 

  15. Pan, T., Jiang, D.Q., Hayat, T., et al.: Extinction and periodic solutions for an impulsive SIR model with incidence rate stochastically perturbed. Physica A 505, 385–397 (2018)

    Article  MATH  Google Scholar 

  16. Liu, C., Liu, M.: Stochastic dynamics in a nonautonomous prey-predator system with impulsive perturbations and L\(\acute{e}\)vy jumps. Commun. Nonlinear Sci. 78, 104851 (2019)

    Article  MATH  Google Scholar 

  17. Cyr, J., Nguyen, P., Temam, R.: Stochastic one layer shallow water equation with L\(\acute{e}\)vy noise. Discrete Cont. Dyn B 24, 3765–3818 (2019)

    MATH  Google Scholar 

  18. Liu, M., Zhu, Y.: Stability of a budworm growth model with random perturbations. Appl Math. Lett. 79, 13–19 (2018)

    Article  MATH  Google Scholar 

  19. Wang, Y.: Analysis of a budworm growth model with jump-diffusion. Physica A 531, 121763 (2019)

    Article  MATH  Google Scholar 

  20. Ji, W., Hu, G.: Stability and explicit stationary density of a stochastic single-species model. Appl. Math. Comput. 390, 125593 (2021)

    MATH  Google Scholar 

  21. Belabbas, M., Ouahab, A., Souna, F.: Rich dynamics in a stochastic predator-prey model with protection zone for the prey and multiplicative noise applied on both species. Nonlinear Dyn. 106, 2761–2780 (2021)

    Article  Google Scholar 

  22. Souna, F., Lakmeche, A.: Spatiotemporal patterns in a diffusive predator–prey system with Leslie–Gower term and social behavior for the prey. Math. Method. Appl. Sci 44, 13920–13944 (2021)

    Article  MATH  Google Scholar 

  23. Lin, G.H., Ji, J.P., Wang, L., et al.: Multitype bistability and long transients in a delayed spruce budworm population model. J. Differ. Equ. 283, 263–289 (2021)

    Article  MATH  Google Scholar 

  24. Tang, X.S.: Periodic solutions and spatial patterns induced by mixed delays in a diffusive spruce budworm model with Holling II predation function. Math Comput. Simul. 192, 420–429 (2022)

    Article  MATH  Google Scholar 

  25. May, R.: Stability and Complexity in Model Ecosystems. Princeton University Press, Princeton (2001)

    Book  MATH  Google Scholar 

  26. Duan, L., Huang, L.H.: Threshold dynamics of a vector-host epidemic model with spatial structure and nonlinear incidence rate. Proc. Am. Math. Soc. 149, 4789–4797 (2021)

    Article  MATH  Google Scholar 

  27. Lv, H.B., Liu, Z.J., Chen, Y.P., et al.: Stochastic permanence of two impulsive stochastic delay single species systems incorporating predation term. J. Appl. Math. Comput. 56, 691–713 (2017)

    Article  MATH  Google Scholar 

  28. Liu, Z.J., Guo, S.L., Tan, R.H., et al.: Modeling and analysis of a non-autonomous single-species model with impulsive and random perturbations. Appl. Math. Model. 40, 5510–5531 (2016)

    Article  MATH  Google Scholar 

  29. Lipster, R.: A strong law of large numbers for local martingale. Stochastics 3, 217–228 (1980)

    Article  Google Scholar 

  30. Hussain, G., Khan, A., Zahri, M., et al.: Stochastic permanence of an epidemic model with a saturated incidence rate. Chaos Soliton. Fract. 139, 110005 (2020)

    Article  MATH  Google Scholar 

  31. Lan, G.J., Wei, C.J., Zhang, S.W.: Long time behaviors of single-species population models with psychological effect and impulsive toxicant in polluted environments. Physica A 521, 828–842 (2019)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Hunan Normal University, Changsha, 410081, Hunan, People’s Republic of China

    Daipeng Kuang, Yubo Liu & Jianli Li

  2. Key Laboratory of High Performance Computing and Stochastic Information Processing (HPCSIP) (Ministry of Education of China), Changsha, Hunan, People’s Republic of China

    Daipeng Kuang, Yubo Liu & Jianli Li

Authors
  1. Daipeng Kuang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yubo Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jianli Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jianli Li.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This work is supported by the NNSF of China (12071105) and the Key Projects of Science Research in University of Anhui Province (KJ2021A1049)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kuang, D., Liu, Y. & Li, J. Analysis of impulsive stochastic delay budworm population model with L\(\acute{\mathrm {e}}\)vy jumps. J. Appl. Math. Comput. 69, 785–810 (2023). https://doi.org/10.1007/s12190-022-01768-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12190-022-01768-1

Keywords

Mathematics Subject Classification

Search

Navigation