An operatorial description of desertification

Fabio Bagarello, Fabio Bagarello, Anna Maria Cherubini, Francesco Oliveri

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)

Abstract

We propose a simple theoretical model for desertification processes based on three actors (soil, seeds, and plants) on a two-dimensional lattice. Each actor is described by a time dependent fermionic operator, and the dynamics is ruled by a self-adjoint Hamilton-like operator. We show that even taking into account only a few parameters, accounting for external actions on the ecosystem or the response to positive feedbacks, the model provides a plausible description of the desertification process, and can be adapted to different ecological landscapes. We first describe the simplified model in one cell. Then, we define the full model on a two-dimensional region, taking into account additional factors such as nonhomogeneities, the competition for resources between plants, and the spread of seeds due to the action of wind or animals. This allows us to explore the effects of positive feedback on slowing down, stopping, or reversing the desertification process.
Original languageEnglish
Pages (from-to)479-499
Number of pages21
JournalSIAM Journal on Applied Mathematics
Volume76
Publication statusPublished - 2016

All Science Journal Classification (ASJC) codes

  • Applied Mathematics

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