JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2026, Vol. 61 ›› Issue (7): 82-92.doi: 10.6040/j.issn.1671-9352.0.2024.297

• Mathematical Biology • Previous Articles    

Forced waves in a predator-prey lattice differential system in a shifting environment

TONG Maosen, ZHOU Rong   

  1. School of Mathematics and Statistics, Xidian University, Xian 710071, Shaanxi, China
  • Published:2026-07-01

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Abstract: In this paper, we study the existence and nonexistence of forced waves in a class of predator-prey lattice differential models in a shifting environment. Firstly, we prove the existence of forced waves for this model by constructing suitable upper and lower solutions and applying Schauder fixed point theorem. Then, we prove the nonexistence of forced wave by using the method of proof by contradiction.

Key words: predator-prey model, Lattice differential system, shifting environment, forced wave

CLC Number: 

  • O175
[1] Berestycki H, Fang J. Forced waves of the Fisher-KPP equation in a shifting environment[J]. Journal of Differential Equations, 2018, 264(3):2157-2183.
[2] Li W T, Wang J B, Zhao X Q. Spatial dynamics of a nonlocal dispersal population model in a shifting environment[J]. Journal of Nonlinear Science, 2018, 28(4):1189-1219.
[3] Wu C F, Wang Y, Zou X F. Spatial-temporal dynamics of a Lotka-Volterra competition model with nonlocal dispersal under shifting environment[J]. Journal of Differential Equations, 2019, 267(8):4890-4921.
[4] Hu H J, Deng L T, Huang J H. Traveling wave of a nonlocal dispersal Lotka-Volterra cooperation model under shifting habitat[J]. Journal of Mathematical Analysis and Applications, 2021, 500(1):125100.
[5] Choi W, Giletti T, Guo J S. Persistence of species in a predator-prey systemwith climate change and either nonlocal or local dispersal[J]. Journal of Differential Equations, 2021, 302:807-853.
[6] Bunimovich L A, Sinai Y G. Spacetime chaos in coupled map lattices[J]. Nonlinearity, 1988, 1(4):491-516.
[7] Hu C B, Li B T. Spatial dynamics for lattice differential equations with a shifting habitat[J]. Journal of Differential Equations, 2015, 259(5):1967-1989.
[8] Wang J B, Zhu J L. Propagation phenomena for a discrete diffusive predator-prey model in a shifting habitat [J]. Journal of Dynamics and Differential Equations, 2024, 36(3):2739-2771.
[9] Chen X F, Guo J S. Uniqueness and existence of traveling waves for discrete quasilinear monostable dynamics[J]. Mathematische Annalen, 2003, 326(1):123-146.
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