Keywords and phrases: predator-prey system, nonlocal intraspecific competition, Hopf bifurcation, diffusion.
Received: September 5, 2023; Accepted: October 11, 2023; Published: November 30, 2023
How to cite this article: Haoming Wu, Zhaoyan Shi and Ming Liu, Hopf bifurcation of a diffusive predator-prey system with nonlocal intraspecific competition, Advances in Differential Equations and Control Processes 30(4) (2023), 395-411. http://dx.doi.org/10.17654/0974324323022
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
References: [1] D. Geng, W. Jiang, Y. Lou and H. Wang, Spatiotemporal patterns in a diffusive predator-prey system with nonlocal intraspecific prey competition, Stud. Appl. Math. 148(1) (2022), 396-432. [2] J. Furter and M. Grinfeld, Local vs. nonlocal interactions in population dynamics, J. Math. Biol. 27(1) (1989), 65-80. [3] G. B. Ermentrout and J. D. Cowan, Secondary bifurcation in neuronal nets, SIAM J. Appl. Math. 39(2) (1980), 323-340. [4] S. Chen, J. Wei and K. Yang, Spatial nonhomogeneous periodic solutions induced by nonlocal prey competition in a diffusive predator-prey model, Int. J. Bifur. Chaos Appl. Sci. Eng. 29(4) (2019), 1950043. [5] S. Chen and J. Yu, Stability and bifurcation on predator-prey systems with nonlocal prey competition, Discrete Contin. Dyn. Syst. 38(1) (2018), 43-62. [6] Q. Shi, J. Shi and Y. Song, Effect of spatial average on the spatiotemporal pattern formation of reaction-diffusion systems, J. Dynam. Differential Equations 34(3) (2022), 2123-2156. [7] H. B. Shi and S. Ruan, Spatial, temporal and spatiotemporal patterns of diffusive predator-prey models with mutual interference, IMA J. Appl. Math. 80(5) (2015), 1534-1580. [8] J. Wang, Spatiotemporal patterns of a homogeneous diffusive predator-prey system with holling type III functional response, J. Dynam. Differential Equations 29(4) (2017), 1383-1409. [9] Y. Song, T. Zhang and Y. Peng, Turing-Hopf bifurcation in the reaction-diffusion equations and its applications, Commun. Nonlinear Sci. Numer. Simul. 33(4) (2016), 229-258. [10] W. Jiang and Q. AN, Turing-Hopf bifurcation and spatio-temporal patterns of a ratio-dependent Holling-Tanner model with diffusion, Internat. J. Bifur. Chaos 28(9) (2018), 1850108. [11] F. Yi, J. Wei and J. Shi, Bifurcation and spatiotemporal patterns in a homogeneous diffusive predator-prey system, J. Differential Equations 246(5) (2009), 1944-1977. [12] R. Yang and Y. Song, Spatial resonance and Turing-Hopf bifurcations in the Gierer-Meinhardt model, Nonlinear Anal. Real World Appl. 31 (2016), 356-387. [13] R. Yuan, W. Jiang and Y. Wang, Saddle-node-Hopf bifurcation in a modified Leslie-Gower predator-prey model with time-delay and prey harvesting, J. Math. Anal. Appl. 422(2) (2015), 1072-1090. [14] X. Chen and W. Jiang, Turing-Hopf bifurcation and multi-stable spatio-temporal patterns in the Lengyel-Epstein system, Nonlinear Anal. Real World Appl. 49 (2019), 386-404. [15] X. Li, W. Jiang and J. Shi, Hopf bifurcation and Turing instability in the reaction-diffusion Holling-Tanner predator-prey model, IMA J. Appl. Math. 78(2) (2013), 287-306. [16] S. Wu and Y. Song, Stability and spatiotemporal dynamics in a diffusive predator-prey model with nonlocal prey competition, Nonlinear Anal. Real World Appl. 48 (2019), 12-39.
|