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Impacts of fear effect and nonlocal competition on a diffusive prey–predator model with delay

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Abstract

Nonlocal prey competition, which describes that intra-prey competition is not only dependent on a location in space but also related to entire space, is introduced to a prey–predator model involving fear effect and digest delay. In the nonlocal prey competition model, the critical delay threshold increases with the increasing of the fear level or the intra-prey competition coefficient. In addition, in the case that the intra-prey competition coefficient is less than the threshold, local and nonlocal prey competition models admit the same critical delay threshold. However, in the case that the intra-prey competition coefficient is beyond the threshold, the critical delay threshold for nonlocal prey competition is less than local prey competition. Moreover, nonlocal prey competition term can drive Hopf bifurcation for spatially inhomogeneous form, and the spatially inhomogeneous periodic solution emerges. It is worth noting that in the absence of delay, nonlocal prey competition model can undergo spatially inhomogeneous Hopf bifurcation and Turing instability by diffusion, but local prey competition can not occur. Numerical simulations verify the theoretical analysis. Also, under the influence of nonlocal effect, the amplitude of the spatially homogeneous periodic solution becomes larger. Meanwhile, nonlocal effect may increase the risk of extinction for two species to a certain extent.

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References

  1. Lotka, A.J.: Fluctuations in the abundance of a species considered mathematically. Nature 119(2983), 12–12 (1927)

    Article  Google Scholar 

  2. Wang, J., Wei, J., Shi, J.: Global bifurcation analysis and pattern formation in homogeneous diffusive predator-prey systems. J. Differ. Equ. 260(4), 3495–3523 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  3. Liu, J., Liu, B., Lv, P., et al.: An eco-epidemiological model with fear effect and hunting cooperation. Chaos Solitons Fractals 142, 110494 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  4. Preisser, E.L., Bolnick, D.I.: The many faces of fear: comparing the pathways and impacts of nonconsumptive predator effects on prey populations. PLoS ONE 3(6), e2465 (2008)

    Article  Google Scholar 

  5. Zanette, L.Y., White, A.F., Allen, M.C., et al.: Perceived predation risk reduces the number of offspring songbirds produce per year. Science 334(6061), 1398–1401 (2011)

    Article  Google Scholar 

  6. Pangle, K.L., Peacor, S.D., Johannsson, O.E.: Large nonlethal effects of an invasive invertebrate predator on zooplankton population growth rate. Ecology 88(2), 402–412 (2007)

    Article  Google Scholar 

  7. Wang, X., Zanette, L., Zou, X.: Modelling the fear effect in predator-prey interactions. J. Math. Biol. 73(5), 1179–1204 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  8. Dong, Y., Wu, D., Shen, C., et al.: Influence of fear effect and predator-taxis sensitivity on dynamical behavior of a predator-prey model. Z. Angew. Math. Phys. 73(1), 1–17 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  9. Liu, J., Kang, Y.: Spatiotemporal dynamics of a diffusive predator–prey model with fear effect. Nonlinear Anal.: Model. Control 27, 1–22 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  10. Okubo, A., Levin, S.A.: Diffusion and Ecological Problems: Modern Perspectives. Springer, New York (2001)

    Book  MATH  Google Scholar 

  11. Song, Y., Peng, Y., Zou, X.: Persistence, stability and Hopf bifurcation in a diffusive ratio-dependent predator–prey model with delay. Int. J. Bifur. Chaos 24(07), 1450093 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  12. Furter, J., Grinfeld, M.: Local vs. non-local interactions in population dynamics. J. Math. Biol. 27(1), 65–80 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  13. Merchant, S.M., Nagata, W.: Instabilities and spatiotemporal patterns behind predator invasions with nonlocal prey competition. Theor. Popul. Biol. 80(4), 289–297 (2011)

    Article  MATH  Google Scholar 

  14. Tian, C., Shi, Q., Cui, X., et al.: Spatiotemporal dynamics of a reaction–diffusion model of pollen tube tip growth. J. Math. Biol. 79(4), 1319–1355 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  15. Hwang, J.U., Gu, Y., Lee, Y.J., et al.: Oscillatory ROP GTPase activation leads the oscillatory polarized growth of pollen tubes. Mol. Biol. Cell 16(11), 5385–5399 (2005)

    Article  Google Scholar 

  16. Chen, S., Yu, J.: Stability and bifurcation on predator–prey systems with nonlocal prey competition. Discrete Contin. Dynam. Systems 38(1), 43 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  17. Chen, S., Wei, J., Yang, K.: Spatial nonhomogeneous periodic solutions induced by nonlocal prey competition in a diffusive predator-prey model. Int. J. Bifur. Chaos 29(04), 1950043 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  18. Wu, S., Song, Y.: Stability and spatiotemporal dynamics in a diffusive predator-prey model with nonlocal prey competition. Nonlinear Anal. Real World Appl. 48, 12–39 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  19. Song, Y., Yang, G.: Spatio-temporal dynamics of a reaction–diffusion equation with the nonlocal spatial average and delay. Appl. Math. Lett. 107, 106388 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  20. Zhang, X., An, Q., Wang, L.: Spatiotemporal dynamics of a delayed diffusive ratio-dependent predator–prey model with fear effect. Nonlinear Dyn. 105(4), 3775–3790 (2021)

    Article  Google Scholar 

  21. Gao, W., Dai, B.: Dynamics of a predator–prey model with delay and fear effect. J. Nonlinear Model. Anal. 1(1), 57–72 (2019)

    Google Scholar 

  22. Wu, S., Song, Y.: Stability and spatiotemporal dynamics in a diffusive predator–prey model with nonlocal prey competition. Nonlinear Anal. Real World Appl. 48, 12–39 (2019)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

The authors thank an anonymous reviewer for helpful comments which improved the original manuscript of the paper. The work is partially supported by the National Natural Science Foundation of China (No 11975025); the Natural Science Foundation of Anhui Province of China (No 2108085MA10).

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  1. Department of Mathematics, Anqing Normal University, Anqing, 246133, China

    Youwei Yang, Daiyong Wu, Chuansheng Shen, Jian Gao & Fengping Lu

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Yang, Y., Wu, D., Shen, C. et al. Impacts of fear effect and nonlocal competition on a diffusive prey–predator model with delay. J. Appl. Math. Comput. 69, 2155–2176 (2023). https://doi.org/10.1007/s12190-022-01827-7

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  • DOI: https://doi.org/10.1007/s12190-022-01827-7

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