Work

Dynamic behavior analysis of vegetation water model with double saturation transformation term

Year: 2026

Type: article

Abstract: In this paper, we propose a vegetation-water system incorporating double saturation transformation terms, which more vividly depicts the mutual influence and transformation relationship between vegetation and water. Firstly, we explore the global stability of boundary equilibrium points. Meanwhile, we investigate the stability of positive equilibria and Turing instability. The results reveal that these equilibria remain unstable when vegetation density reaches the minimum value, and Turing instability occurs under conditions of low vegetation diffusion or high water diffusion coefficients. Secondly, by applying the maximum principle, we derive a priori estimates for nonnegative steady-state solutions. Thirdly, we discuss the bifurcation phenomena associated with simple and double eigenvalues, and provide criteria for determining the direction of bifurcation using the Lyapunov-Schmidt reduction method. Finally, through numerical simulation, we validate the theoretical results, examine the dynamic behavior near bifurcation thresholds, and illustrate the changes in vegetation configurations under different parameter scenarios.

Source: Advances in Continuous and Discrete Models

DOI: 10.1186/s13662-026-04075-2

Authors: Xiaozhou Feng, Xuanye Sheng, Wenhao Jiang, Ming Xu, Changtong Li, Fei Xie

Institution: Xi'an Technological University

Language: English

Topic: Ecosystem dynamics and resilience

Subfield: Global and Planetary Change

Field: Environmental Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $1,890

Funder: National Natural Science Foundation of China