Vegetation Patterns: Structures and Dynamics

Abstract

Vegetation patterns are a hallmark of ecosystem self-organization, emerg- ing from the intrinsic dynamics of nonlinear feedback mechanisms and spatiotem- poral interactions. This review systematically explores and examines the structural characteristics of these patterns, the phenomena of multistability, and their implica- tions for ecosystem stability through the lens of mathematical modeling and dynam- ical systems theory. In particular, reaction-diffusion models serve as a key analytical tool, revealing how local positive feedback and non-local negative feedback drive self- organized spatial structures via Turing bifurcation. Bifurcation theory and potential landscape analysis further elucidate ecosystem multistability, quantifying critical tran- sitions among uniform vegetation, patterned states, and bare soil under environmen- tal conditions. Advances in spatial metrics, including traditional statistical measures (e.g. variance, autocorrelation) and emerging complexity-based indicators (e.g. hyper- uniformity, spatial permutation entropy) provide robust methods for detecting ecolog- ical functional shifts and early-warning signs of regime shifts. Additionally, restoration strategies grounded in structural optimization, such as optimal control theory, offer a theoretical framework for vegetation pattern reconstruction and stability regulation, particularly in arid and semi-arid regions. Future research should integrate multiscale modeling and interdisciplinary approaches to deepen our understanding of vegetation structure-function relationships. Such efforts will yield both theoretical insights and practical solutions for mitigating global ecological degradation and climate change.

Keywords

Vegetation patterns / ecosystem stability / multistability / optimal control / critical tran-sitions

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