Skip to main content
SpringerLink
Log in

Spatiotemporal dynamics induced by nonlocal competition in a diffusive predator-prey system with habitat complexity

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

In this paper, we study a delayed diffusive predator–prey model with nonlocal competition in prey and habitat complexity. The local stability of coexisting equilibrium is studied by analyzing the eigenvalue spectrum. Time delay inducing Hopf bifurcation is investigated by using time delay as bifurcation parameter. We give some conditions for determining the bifurcation direction and the stability of the bifurcating periodic solution by utilizing the normal form method and center manifold theorem. Our results suggest that only nonlocal competition and diffusion together can induce stably spatial inhomogeneous bifurcating periodic solutions.

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
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  1. Zhou, Y., Yan, X., Zhang, C.: Turing patterns induced by self-diffusion in a predator-prey model with schooling behavior in predator and prey. Nonlinear Dyn. 105, 3731–3747 (2021)

    Article  Google Scholar 

  2. Du, Y., Hsu, S.B.: A diffusive predator-prey model in heterogeneous environment. J. Differ. Equ. 203(2), 331–364 (2004)

    Article  MathSciNet  Google Scholar 

  3. Freedman, H.I., Rao, V.: The trade-off between mutual interference and time lags in predator-prey systems. Bull. Math. Biol. 45(6), 991–1004 (1983)

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  5. Wang, L., Zhang, M., Jia, M.: A delayed predator-prey model with prey population guided anti-predator behaviour and stage structure. J. Appl. Anal. Comput. 11(4), 1811–1824 (2020)

    MathSciNet  Google Scholar 

  6. Volterra, V.: Fluctuations in the abundance of species considered mathematically. Nature 118(2972), 558–560 (1926)

    Article  Google Scholar 

  7. Yang, R., Song, Q., An, Y.: Spatiotemporal dynamics in a predator-prey model with functional response increasing in both predator and prey densities. Mathematics 10(1), 17 (2021)

    Article  MathSciNet  Google Scholar 

  8. Maji, C.: Impact of fear effect in a fractional-order predator-prey system incorporating constant prey refuge. Nonlinear Dyn. 107, 1329–1342 (2022)

    Article  Google Scholar 

  9. Yang, R., Zhao, X., An, Y.: Dynamical analysis of a delayed diffusive predator-prey model with additional food provided and anti-predator behavior. Mathematics 10(3), 469 (2022)

    Article  Google Scholar 

  10. Holling, C.S.: The functional response of predators to prey density and its role in mimicry and population dynamics. Mem. Entomol. Soc. Can 97(45), 1–60 (1965)

    Google Scholar 

  11. Beddington, J.R.: Mutual interference between parasites or predators and its effect on searching efficiency. J. Anim. Ecol. 44(1), 331–340 (1975)

    Article  Google Scholar 

  12. Crowley, P.H., Martin, E.K.: Functional responses and interference within and between year classes of a dragonfly population. J. N. Am. Benthol. Soc. 8(3), 211–221 (1989)

    Article  Google Scholar 

  13. Hassell, M.P., Varley, G.C.: New inductive population model for insect parasites and its bearing on biological control. Nature 223(5211), 1133–1137 (1969)

    Article  Google Scholar 

  14. Li, Y., Liu, H., Yang, R.: Time-delay effect on a diffusive predator-prey model with habitat complexity. Adv. Differ. Equ. 2021(1), 1–24 (2021)

    Article  MathSciNet  Google Scholar 

  15. Wang, S., Tang, H., Ma, Z.: Hopf bifurcation of a multiple-delayed predator-prey system with habitat complexity. Math. Comput. Simul. 180, 1–23 (2021)

    Article  MathSciNet  Google Scholar 

  16. Ma, Z.: Hopf bifurcation of a generalized delay-induced predator-prey system with habitat complexity. Int. J. Bifurc. Chaos 30(06), 1495–1507 (2020)

    Article  MathSciNet  Google Scholar 

  17. Eklv, P.: Effects of habitat complexity and prey abundance on the spatial and temporal distributions of perch (Perca fluviatilis) and pike (Esox lucius). Canad. J. Fisher. Aquat. Sci. 54(54), 1520–1531 (1997)

    Article  Google Scholar 

  18. August, P.V.: The role of habitat complexity and heterogeneity. Ecology 64(6), 1495–1507 (2008)

    Article  Google Scholar 

  19. Canion, C.R., Heck, K.L.: Effect of habitat complexity on predation success: re-evaluating the current paradigm in seagrass beds. Mar. Ecol. Prog. 393(393), 37–46 (2009)

    Article  Google Scholar 

  20. Jana, D., Bairagi, N.: Habitat complexity, dispersal and metapopulations: macroscopic study of a predator-prey system. Ecol. Complex. 17, 131–139 (2014)

    Article  Google Scholar 

  21. Ma, Z., Wang, S.: A delay-induced predator-prey model with Holling type functional response and habitat complexity. Nonlinear Dyn. 93, 1519–1544 (2018)

    Article  Google Scholar 

  22. Song, Y., Peng, Y., Zhang, T.: The spatially inhomogeneous Hopf bifurcation induced by memory delay in a memory-based diffusion system. J. Differ. Equ. 300, 597–624 (2021)

    Article  MathSciNet  Google Scholar 

  23. Yi, F.: Turing instability of the periodic solutions for reaction-diffusion systems with cross-diffusion and the patch model with cross-diffusion-like coupling. J. Differ. Equ. 281, 379–410 (2021)

    Article  MathSciNet  Google Scholar 

  24. Britton, N.F.: Aggregation and the competitive exclusion principle. J. Theor. Biol. 136(1), 57–66 (1989)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  26. Chen, S., Yu, J.: Stability and bifurcation on predator-prey systems with nonlocal prey competition. Discrete Contin. Dyn. Syst. 38(1), 43–62 (2018)

    Article  MathSciNet  Google Scholar 

  27. Geng, D., Jiang, W., Lou, Y, et al.: Spatiotemporal patterns in a diffusive predator-prey system with nonlocal intraspecific prey competition. Stud. Appl. Math. 1–37 (2021)

  28. Liu, Y., Duan, D., Niu, B.: Spatiotemporal dynamics in a diffusive predator-prey model with group defense and nonlocal competition. Appl. Math. Lett. 103, 106175 (2020)

    Article  MathSciNet  Google Scholar 

  29. Wu, J.: Theory and Applications of Partial Functional Differential Equations. Springer, Berlin (1996)

    Book  Google Scholar 

  30. Hassard, B.D., Kazarinoff, N.D., Wan, Y.H.: Theory and Applications of Hopf Bifurcation. Cambridge University Press, Cambridge, New York (1981)

    MATH  Google Scholar 

  31. Jost, C., Ellner, S.P.: Testing for predator dependence in predator-prey dynamics: a non-parametric approach. Proc. R. Soc. B 267, 1611–1620 (2000)

    Article  Google Scholar 

  32. Harrison, G.W.: Comparing predator-prey models to Luckinbill’s experiment with Didinium and Paramecium. Ecology 76(2), 357–374 (1995)

  33. Luckinbill, L.S.: Coexistence in laboratory populations of Paramecium aurelia and its predator Didinium nasutum. Ecology 54, 1320–1327 (1973)

    Article  Google Scholar 

  34. Salt, G.W.: Predator and prey densities as controls of the rate of capture by the predator Didinium nasutum. Ecology 55, 434–439 (1974)

  35. Reukauf E. Zur biologie von Didinium nasutum. Zeitschrift für vergleichende Physiologie 11, 689–701 (1930)

  36. Butzel, H.M., Bolten, A.B.: The relationship of the nutritive state of the prey organism Paramecium aurelia to the growth and encystment of Didinium nasutum. J. Protozool. 15, 256–258 (1968)

    Article  Google Scholar 

Download references

Funding

This research is supported by the Fundamental Research Funds for the Central Universities (Grant No. 2572022DJ05), Postdoctoral program of Heilongjiang Province (No. LBH-Q21060), and College Students Innovations Special Project funded by Northeast Forestry University (No. 202210225157), National Nature Science Foundation of China (No. 11601070) and Heilongjiang Provincial Natural Science Foundation (No. A2018001).

Author information

Authors and Affiliations

  1. Department of Mathematics, Northeast Forestry University, Harbin, 150040, Heilongjiang, China

    Ruizhi Yang, Chenxuan Nie & Dan Jin

Authors
  1. Ruizhi Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chenxuan Nie
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Dan Jin
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors contributed to the study conception and design. Material preparation, data collection, and analysis were performed by Ruizhi Yang. Numerical simulations were performed by Ruizhi Yang and Chenxuan Nie. All authors read and approved the final manuscript.

Corresponding author

Correspondence to Dan Jin.

Ethics declarations

Conflict of interest

The authors have no relevant financial or non-financial interests to disclose.

Data availability

Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study.

Additional information

Publisher's Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yang, R., Nie, C. & Jin, D. Spatiotemporal dynamics induced by nonlocal competition in a diffusive predator-prey system with habitat complexity. Nonlinear Dyn 110, 879–900 (2022). https://doi.org/10.1007/s11071-022-07625-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-022-07625-x

Keywords

Search

Navigation