# American Institute of Mathematical Sciences

October  2014, 34(10): 4107-4126. doi: 10.3934/dcds.2014.34.4107

## Biodiversity and vulnerability in a 3D mutualistic system

 1 Universidad Central del Ecuador, Ciudadela Universitaria, Av. América S/N, Quito, Ecuador 2 Departamento de Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, Universidad de Sevilla, Calle Tarfia s/n, 41012-Seville, Spain 3 Dpto. de Ecuaciones Diferenciales y Análisis Numérico, Fac. de Matemáticas, Univ. de Sevilla, C/. Tarfia s/n, 41012 - Sevilla

Received  January 2013 Revised  February 2013 Published  April 2014

In 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.
Citation: Giovanny Guerrero, José Antonio Langa, Antonio Suárez. Biodiversity and vulnerability in a 3D mutualistic system. Discrete & Continuous Dynamical Systems - A, 2014, 34 (10) : 4107-4126. doi: 10.3934/dcds.2014.34.4107
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