A Multiscale Approach for vegetation patterning
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Vegetation patterns in semi-arid ecosystems often emerge through self-organization driven by feedbacks between biomass, water, and soil properties. Among these, negative plant-soil interactions such as autotoxicity play a crucial role in shaping spatial organization and ecosystem resilience [Mazzoleni et al., Commun. Ecol., 8, 103-109, 2007]. In this talk, we investigate how autotoxicity interacts with climate change to shape pattern dynamics across different distances from the onset of instability. Starting from a generalized Klausmeier-type model [Klausmeier C.A., Science, 284, 1826--1828, 1999], we perform a multiscale analysis to characterize regimes ranging from near-threshold oscillatory bands to far-from-equilibrium traveling pulses [Consolo G., Grifò G., Valenti G., Physica D, 459, 134020, 2024; Grifò G., Iuorio A., Veerman F., SIAM Journal on Applied Mathematics, 85, 188-209, 2025]. Through linear stability analysis, we characterize the parameter region where uniform vegetation becomes unstable, revealing that increasing autotoxicity enlarges the domain of patterned states and promotes wave-type instabilities. A weakly nonlinear multiple-scale analysis near onset shows that autotoxicity can alter the bifurcation structure, potentially leading to subcritical dynamics and large-amplitude migrating bands even under moderate environmental stress. Far from the instability threshold, numerical simulations highlight the emergence of localized traveling pulses whose morphology and propagation speed do not depend on toxicity strength. These pulses exhibit multiscale spatial profiles and originate from the desert state, mimicking severe degradation scenarios. Our findings demonstrate that autotoxicity acts as a destabilizing mechanism that not only triggers pattern formation but also controls transitions between different dynamical regimes. From an ecological perspective, this suggests that negative feedbacks mediated by toxic compounds may accelerate desertification under decreasing rainfall or increasing plant mortality. The proposed framework provides new insights into the role of plant-soil interactions in dryland ecosystems and lays the groundwork for future studies on resilience and restoration strategies under climate change.
