Fragmentation followed by desertification in water-limited resources and/or nutrient-poor ecosystems is a major risk to the biological productivity of vegetation. By using the vegetation interaction-redistribution model, we analyse the interaction between localised vegetation patches. Here we show analytically and numerically that the interaction between two or more patches is always repulsive. As a consequence, only a single localised vegetation patch is stable, and other localised bounded states or clusters of them are unstable. Following this, we discuss the impact of the repulsive nature of the interaction on the formation and the selection of vegetation patterns in fragmented ecosystems.
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Fruitful discussions with Profs. R. Lefever, K. Panajotov, and S. S. Gopalakrishnan are gratefully acknowledged. MGC thanks for the financial support of FONDECYT projects 1180903, 1150507 and Millennium Institute for Research in Optics (MIRO). E.B.C. thanks, the financial support of CONICYT though Becas Magister Nacional 2015, Contract no. 22151824. M.T. received support from the Fonds National de la Recherche Scientifique (Belgium). The authors gratefully acknowledge the financial support of Wallonie-Bruxelles International (WBI). DE thanks for the financial support of FONDECYT projects 1170669.
© 2020, The Author(s).