Guerrero Suárez, Giovanny FabiánLanga Rosado, José AntonioSuárez Fernández, Antonio2016-04-202016-04-202014-10Guerrero Suárez, G.F., Langa Rosado, J.A. y Suárez Fernández, A. (2014). Biodiversity and vulnerability in a 3D mutualistic system.1078-09471553-5231http://hdl.handle.net/11441/40115In this paper we study a three dimensional mutualistic model of two plants in competition and a pollinator with cooperative relation with plants. We compare the dynamical properties of this system with the associated one under absence of the pollinator. We observe how cooperation is a common fact to increase biodiversity, which it is known that, generically, holds for general mutualistic dynamical systems in Ecology as introduced in [4]. We also give mathematical evidence on how a cooperative species induces an increased biodiversity, even if the species is push to extinction. For this fact, we propose a necessary change in the model formulation which could explain this kind of phenomenon.application/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/3D mutualistic modelIncreasing biodiversityVulnerabilityPermanenceGlobal stabilityinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccesshttps://doi.org/10.3934/dcds.2014.34.4107