Modeling and Nonlinear Analysis of Plant–Soil Moisture Interactions for Sustainable Land Management: Insights for Desertification Mitigation

This research explores the dynamics of vegetation patterns under changing environmental conditions, considering the United Nations Sustainable Development Goal 15: “Protect, restore, and promote the sustainable use of terrestrial ecosystems; combat desertification; halt and reverse land degradation; and prevent biodiversity loss”. In this context, this study presents a modeling and nonlinear analysis framework for plant–soil-moisture interactions, including Holling-II functional response and hyperbolic mortality models. The primary goal is to explore how nonlinear soil–water interactions influence vegetation patterns in semi-arid ecosystems. Moreover, the influence of nonlinear soil–water interaction on the establishment of population patterns is investigated. The formation and evolution of these patterns are explored using theoretical analysis and numerical simulations, as well as important factors and critical thresholds. These insights are crucial for addressing desertification, a key challenge in semi-arid regions that threatens biodiversity, ecosystem services, and sustainable land management. The model, which includes environmental parameters such as rainfall, plant growth rates, and soil moisture, was tested using both theoretical analysis and numerical simulations. These characteristics are carefully adjusted to find important thresholds influencing the danger of desertification. Simulation scenarios, run under set initial conditions and varying parameters, yield useful insights into the pattern of patch development under dynamically changing environmental conditions. The findings revealed that changes in environmental conditions, such as rainfall and plant growth rates, prompted Hopf bifurcation, resulting in the production of three distinct patterns: a dotted pattern, a striped pattern, and a combination of both. The creation of these patterns provides essential information about the sustainability of environmental equilibrium. The variation curve of the average plant biomass reveals that the biomass fluctuates around a constant period, with the amplitude initially increasing, then decreasing, and gradually stabilizing. This research provides a solid foundation for addressing desertification risks, using water resources responsibly, and contributing to a better understanding of ecosystem stability.