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Bifurcation and stability analysis of a cross‐diffusion vegetation‐water model with mixed delays
Author(s) -
Xiong Zixiao,
Zhang Qimin,
Kang Ting
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7384
Subject(s) - mathematics , hopf bifurcation , desertification , stability (learning theory) , vegetation (pathology) , bifurcation , economic shortage , surface water , diffusion , environmental science , thermodynamics , nonlinear system , environmental engineering , ecology , computer science , medicine , linguistics , philosophy , physics , pathology , quantum mechanics , machine learning , government (linguistics) , biology
With desertification becoming more and more serious all over the world, it is crucial to understand the intrinsic relationship between vegetation and water (soil water and surface water). In this paper, a cross‐diffusion model with mixed delays is established to describe the dynamics of vegetation, soil water, and surface water in the case of water shortage. The local stability conditions of positive equilibrium point is established by using Routh–Hurwitz criterion. Then, the conditions for generating Hopf bifurcation are studied. In the end, numerical simulations are carried out to illustrate the effectiveness of the theoretical analysis.