American Institute of Mathematical Sciences

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

Biodiversity and vulnerability in a 3D mutualistic system

Giovanny Guerrero 1, , José Antonio Langa 2, and  Antonio Suárez 3,

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.
Keywords: increasing biodiversity, 3D mutualistic model, global stability., permanence, vulnerability.
Mathematics Subject Classification: Primary: 92B05, 34A34, 34D05, 34D2.
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
References:
[1]

Proc. Natl Acad. Sci. USA, 100 (2003), 9383-9387. doi: 10.1073/pnas.1633576100.  Google Scholar

[2]

Science, 312 (2006), 431-433. doi: 10.1126/science.1123412.  Google Scholar

[3]

Annu. Rev. Ecol. Evol. Syst., 38 (2007), 567-593. Google Scholar

[4]

Nature, 458 (2009), 1018-1020. doi: 10.1038/nature07950.  Google Scholar

[5]

Wiley Series in Mathematical and Computational Biology, John Wiley & Sons, Ltd., Chichester, 2003. doi: 10.1002/0470871296.  Google Scholar

[6]

J. Math. Biology, 16 (1982), 25-31. doi: 10.1007/BF00275158.  Google Scholar

[7]

The American Naturalist, 111 (1977), 135-143. doi: 10.1086/283384.  Google Scholar

[8]

The American Naturalist, 113 (1979), 261-275. doi: 10.1086/283384.  Google Scholar

[9]

Monatsch. Math., 98 (1984), 267-275. doi: 10.1007/BF01540776.  Google Scholar

[10]

Springer, New York, 1993 doi: 10.1007/b98869.  Google Scholar

[11]

Nature, 478 (2011), 233-235. doi: 10.1038/nature10433.  Google Scholar

[12]

SIAM J. Appl. Math., 46 (1986), 856-874. doi: 10.1137/0146052.  Google Scholar

[13]

Nature (News and View), 458 (2009), 979-980. doi: 10.1038/458979a.  Google Scholar

[14]

World Scientific Publishing Co., Inc., River Edge, NJ, 1996. doi: 10.1142/9789812830548.  Google Scholar

[15]

Physica A, 339 (2004), 609-620. doi: 10.1016/j.physa.2004.03.067.  Google Scholar

show all references

References:
[1]

Proc. Natl Acad. Sci. USA, 100 (2003), 9383-9387. doi: 10.1073/pnas.1633576100.  Google Scholar

[2]

Science, 312 (2006), 431-433. doi: 10.1126/science.1123412.  Google Scholar

[3]

Annu. Rev. Ecol. Evol. Syst., 38 (2007), 567-593. Google Scholar

[4]

Nature, 458 (2009), 1018-1020. doi: 10.1038/nature07950.  Google Scholar

[5]

Wiley Series in Mathematical and Computational Biology, John Wiley & Sons, Ltd., Chichester, 2003. doi: 10.1002/0470871296.  Google Scholar

[6]

J. Math. Biology, 16 (1982), 25-31. doi: 10.1007/BF00275158.  Google Scholar

[7]

The American Naturalist, 111 (1977), 135-143. doi: 10.1086/283384.  Google Scholar

[8]

The American Naturalist, 113 (1979), 261-275. doi: 10.1086/283384.  Google Scholar

[9]

Monatsch. Math., 98 (1984), 267-275. doi: 10.1007/BF01540776.  Google Scholar

[10]

Springer, New York, 1993 doi: 10.1007/b98869.  Google Scholar

[11]

Nature, 478 (2011), 233-235. doi: 10.1038/nature10433.  Google Scholar

[12]

SIAM J. Appl. Math., 46 (1986), 856-874. doi: 10.1137/0146052.  Google Scholar

[13]

Nature (News and View), 458 (2009), 979-980. doi: 10.1038/458979a.  Google Scholar

[14]

World Scientific Publishing Co., Inc., River Edge, NJ, 1996. doi: 10.1142/9789812830548.  Google Scholar

[15]

Physica A, 339 (2004), 609-620. doi: 10.1016/j.physa.2004.03.067.  Google Scholar

[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, José María Iriondo, José 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, José M. Iriondo, José 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

2019 Impact Factor: 1.338

Tools

Metrics

  • PDF downloads (25)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences