Resource-consumer dynamics in drylands : Modeling the role of plant-plant facilitation-competition shifts with a piecewise system
Da Cruz, Leonardo Pereira Costa (Universidade de São Paulo)
Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Berdugo, Miguel (Universidad Complutense de Madrid. Departamento de Biodiversidad, Ecología y Evolución)
Sardanyés, Josep (Centre de Recerca Matemàtica)

Date:	2025
Abstract:	In drylands, water availability determines plant population densities and whether they cooperate via facilitation or compete. When water scarcity intensifies, plant densities decrease and competition for water surpasses the benefits of soil improvement by facilitator plants, involving an abrupt shift from facilitation to competition. Here, we model this facilitation-competition shift using a piecewise system in a resource species such as grasses studying its impact on a resource-consumer dynamical system. First, the dynamics of each system i. e. , competitive and cooperative, are introduced separately for this resource-consumer system. The competitive system, by setting conditions to have a monodromic equilibrium in the first quadrant, has no limit cycles. With a monodromy condition in the same quadrant, the cooperative system only has a hyperbolic, small amplitude limit cycle, allowing for an oscillating coexistence. The dynamic properties of the piecewise system become richer. We here prove the extension of the center-focus problem in this particular case, and from a weak focus of order three, we find 3 limit cycles arising from it. We also study the case assuming continuity in the piecewise system. Finally, we present a special and restricted way of obtaining a limit cycle of small amplitude in a pseudo-Hopf bifurcation type. Our results suggest that abrupt density-dependent functional shifts, such as those described in drylands, could introduce novel dynamical phenomena in population dynamis. Our work also provides a novel theoretical framework to model and investigate population dynamics where ecological interactions change due to density-dependent effects.
Grants:	Agència de Gestió d'Ajuts Universitaris i de Recerca 2021/SGR-00113 Agencia Estatal de Investigación PID2022-136613NB-I00 Ministerio de Ciencia e Innovación RYC-2017-22243 Ministerio de Ciencia e Innovación RYC-2021-031797-I Agencia Estatal de Investigación CEX2020-001084-M European Commission 777911
Note:	Altres ajuts: CERCA Programme/Generalitat de Catalunya
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Published in:	Physica D. Nonlinear phenomena, Vol. 473 (March 2025) , art. 134548, ISSN 1872-8022

DOI: 10.1016/j.physd.2025.134548

Available from: 2027-03-31 Postprint

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Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
Articles > Published articles