# 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, 2014, 34 (10) : 4107-4126. doi: 10.3934/dcds.2014.34.4107
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##### References:
 [1] Yingdan Ji, Wen Tan. Global well-posedness of a 3D Stokes-Magneto equations with fractional magnetic diffusion. Discrete & Continuous Dynamical Systems - B, 2021, 26 (6) : 3271-3278. doi: 10.3934/dcdsb.2020227 [2] Shihu Li, Wei Liu, Yingchao Xie. Large deviations for stochastic 3D Leray-$\alpha$ model with fractional dissipation. Communications on Pure & Applied Analysis, 2019, 18 (5) : 2491-2509. doi: 10.3934/cpaa.2019113 [3] Tomoyuki Tanaka, Kyouhei Wakasa. On the critical decay for the wave equation with a cubic convolution in 3D. Discrete & Continuous Dynamical Systems, 2021  doi: 10.3934/dcds.2021048 [4] Wenjing Liu, Rong Yang, Xin-Guang Yang. Dynamics of a 3D Brinkman-Forchheimer equation with infinite delay. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021052 [5] Thomas Y. Hou, Ruo Li. Nonexistence of locally self-similar blow-up for the 3D incompressible Navier-Stokes equations. Discrete & Continuous Dynamical Systems, 2007, 18 (4) : 637-642. doi: 10.3934/dcds.2007.18.637 [6] Yongming Luo, Athanasios Stylianou. On 3d dipolar Bose-Einstein condensates involving quantum fluctuations and three-body interactions. Discrete & Continuous Dynamical Systems - B, 2021, 26 (6) : 3455-3477. doi: 10.3934/dcdsb.2020239 [7] Guodong Wang, Bijun Zuo. Energy equality for weak solutions to the 3D magnetohydrodynamic equations in a bounded domain. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021078 [8] Qiao Liu. Partial regularity and the Minkowski dimension of singular points for suitable weak solutions to the 3D simplified Ericksen–Leslie system. Discrete & Continuous Dynamical Systems, 2021  doi: 10.3934/dcds.2021041 [9] Francis Hounkpe, Gregory Seregin. An approximation of forward self-similar solutions to the 3D Navier-Stokes system. Discrete & Continuous Dynamical Systems, 2021  doi: 10.3934/dcds.2021059 [10] Luigi C. Berselli, Jishan Fan. Logarithmic and improved regularity criteria for the 3D nematic liquid crystals models, Boussinesq system, and MHD equations in a bounded domain. Communications on Pure & Applied Analysis, 2015, 14 (2) : 637-655. doi: 10.3934/cpaa.2015.14.637 [11] Juan Manuel Pastor, Javier García-Algarra, Javier Galeano, José María Iriondo, José J. Ramasco. A simple and bounded model of population dynamics for mutualistic networks. Networks & Heterogeneous Media, 2015, 10 (1) : 53-70. doi: 10.3934/nhm.2015.10.53 [12] Shangzhi Li, Shangjiang Guo. Permanence and extinction of a stochastic SIS epidemic model with three independent Brownian motions. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2693-2719. doi: 10.3934/dcdsb.2020201 [13] Rafael Luís, Sandra Mendonça. A note on global stability in the periodic logistic map. Discrete & Continuous Dynamical Systems - B, 2020, 25 (11) : 4211-4220. doi: 10.3934/dcdsb.2020094 [14] Lakmi Niwanthi Wadippuli, Ivan Gudoshnikov, Oleg Makarenkov. Global asymptotic stability of nonconvex sweeping processes. Discrete & Continuous Dynamical Systems - B, 2020, 25 (3) : 1129-1139. doi: 10.3934/dcdsb.2019212 [15] Liangliang Ma. Stability of hydrostatic equilibrium to the 2D fractional Boussinesq equations. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021068 [16] Simão Correia, Mário Figueira. A generalized complex Ginzburg-Landau equation: Global existence and stability results. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021056 [17] Michael Grinfeld, Amy Novick-Cohen. Some remarks on stability for a phase field model with memory. Discrete & Continuous Dynamical Systems, 2006, 15 (4) : 1089-1117. doi: 10.3934/dcds.2006.15.1089 [18] Juan Manuel Pastor, Javier García-Algarra, José M. Iriondo, José J. Ramasco, Javier Galeano. Dragging in mutualistic networks. Networks & Heterogeneous Media, 2015, 10 (1) : 37-52. doi: 10.3934/nhm.2015.10.37 [19] Rui Hu, Yuan Yuan. Stability, bifurcation analysis in a neural network model with delay and diffusion. Conference Publications, 2009, 2009 (Special) : 367-376. doi: 10.3934/proc.2009.2009.367 [20] Wei Wang, Wanbiao Ma, Xiulan Lai. Sufficient conditions for global dynamics of a viral infection model with nonlinear diffusion. Discrete & Continuous Dynamical Systems - B, 2021, 26 (7) : 3989-4011. doi: 10.3934/dcdsb.2020271

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