ABSTRACT
Equipped with the tools of pattern formation theory and the model equations (9.10)–(9.14) for water limited vegetation, we can now study vegetation patchiness as a pattern-formation phenomenon. Linear stability analysis can tell us, for example, whether vegetation patchiness arises from a non-uniform instability of uniform vegetation as the precipitation rate decreases below a critical value. Numerical studies can confirm whether the pattern that appears beyond the instability point is a hexagonal pattern and whether the instability is subcritical, as the analysis of the SH equation in Section 7.1 predicts. These aspects of uniform and patterned vegetation states and the complete sequence of such states along the rainfall gradient are studied in Section 10.1.1 for flat terrains and in Section 10.1.2 for sloped terrains. In Section 10.1.3 we consider bistability ranges, where two alternative stable states coexist, and study
an intriguing dynamical aspect of such ranges that occur on slopes, namely, the possible induction of global state transitions between alternative stable vegetation patterns by local disturbances. The pattern-formation approach to dryland vegetation also suggests a novel operational view of the concept of aridity and of the definitions of aridity classes, which we discuss in Section 10.1.4.
