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Attractors for a double time-delayed 2D-Navier-Stokes model
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 |
References:
[1] |
J. Bascompte, P. Jordano, C. J. Melián and J. M. Olesen, The nested assembly of plant-animal mutualistic networks, Proc. Natl Acad. Sci. USA, 100 (2003), 9383-9387.
doi: 10.1073/pnas.1633576100. |
[2] |
J. Bascompte, P. Jordano and J. M. Olesen, Asymmetric coevolutionary networks facilitate biodiversity maintenance, Science, 312 (2006), 431-433.
doi: 10.1126/science.1123412. |
[3] |
J. Bascompte and P. Jordano, The structure of plant-animal mutualistic networks: The architecture of biodiversity, Annu. Rev. Ecol. Evol. Syst., 38 (2007), 567-593. |
[4] |
U. Bastolla, M. A. Fortuna, A. Pascual-García, A. Ferrera, B. Luque and J. Bascompte, The architecture of mutualistic networks minimizes competition and increases biodiversity, Nature, 458 (2009), 1018-1020.
doi: 10.1038/nature07950. |
[5] |
R. S. Cantrell and C. Cosner, Spatial Ecology Via Reaction-Diffusion Equations, Wiley Series in Mathematical and Computational Biology, John Wiley & Sons, Ltd., Chichester, 2003.
doi: 10.1002/0470871296. |
[6] |
C. E. Clark and T. G. Hallam, The community matrix in three species community models, J. Math. Biology, 16 (1982), 25-31.
doi: 10.1007/BF00275158. |
[7] |
B. S. Goh, Stability in models of mutualism, The American Naturalist, 111 (1977), 135-143.
doi: 10.1086/283384. |
[8] |
B. S. Goh, Stability in models of mutualism, The American Naturalist, 113 (1979), 261-275.
doi: 10.1086/283384. |
[9] |
V. Hutson, A theorem on average Lyapunov functions, Monatsch. Math., 98 (1984), 267-275.
doi: 10.1007/BF01540776. |
[10] |
J. D. Murray, Mathematical Biology, Springer, New York, 1993
doi: 10.1007/b98869. |
[11] |
S. Saavedra, D. B. Stouffer, B. Uzzi and J. Bascompte, Strong contributors to network persistence are the most vulnerable to extinction, Nature, 478 (2011), 233-235.
doi: 10.1038/nature10433. |
[12] |
H. L. Smith, Competing subcommunities of mutualists and a generalized Kamke theorem, SIAM J. Appl. Math., 46 (1986), 856-874.
doi: 10.1137/0146052. |
[13] |
G. Sugihara and H. Ye, Cooperative network dynamics, Nature (News and View), 458 (2009), 979-980.
doi: 10.1038/458979a. |
[14] |
Y. Takeuchi, Global Dynamical Properties of Lotka-Volterra Systems, World Scientific Publishing Co., Inc., River Edge, NJ, 1996.
doi: 10.1142/9789812830548. |
[15] |
Y. Wang and H. Wu, Dynamics of a cooperation-competition model for the WWW market, Physica A, 339 (2004), 609-620.
doi: 10.1016/j.physa.2004.03.067. |
show all references
References:
[1] |
J. Bascompte, P. Jordano, C. J. Melián and J. M. Olesen, The nested assembly of plant-animal mutualistic networks, Proc. Natl Acad. Sci. USA, 100 (2003), 9383-9387.
doi: 10.1073/pnas.1633576100. |
[2] |
J. Bascompte, P. Jordano and J. M. Olesen, Asymmetric coevolutionary networks facilitate biodiversity maintenance, Science, 312 (2006), 431-433.
doi: 10.1126/science.1123412. |
[3] |
J. Bascompte and P. Jordano, The structure of plant-animal mutualistic networks: The architecture of biodiversity, Annu. Rev. Ecol. Evol. Syst., 38 (2007), 567-593. |
[4] |
U. Bastolla, M. A. Fortuna, A. Pascual-García, A. Ferrera, B. Luque and J. Bascompte, The architecture of mutualistic networks minimizes competition and increases biodiversity, Nature, 458 (2009), 1018-1020.
doi: 10.1038/nature07950. |
[5] |
R. S. Cantrell and C. Cosner, Spatial Ecology Via Reaction-Diffusion Equations, Wiley Series in Mathematical and Computational Biology, John Wiley & Sons, Ltd., Chichester, 2003.
doi: 10.1002/0470871296. |
[6] |
C. E. Clark and T. G. Hallam, The community matrix in three species community models, J. Math. Biology, 16 (1982), 25-31.
doi: 10.1007/BF00275158. |
[7] |
B. S. Goh, Stability in models of mutualism, The American Naturalist, 111 (1977), 135-143.
doi: 10.1086/283384. |
[8] |
B. S. Goh, Stability in models of mutualism, The American Naturalist, 113 (1979), 261-275.
doi: 10.1086/283384. |
[9] |
V. Hutson, A theorem on average Lyapunov functions, Monatsch. Math., 98 (1984), 267-275.
doi: 10.1007/BF01540776. |
[10] |
J. D. Murray, Mathematical Biology, Springer, New York, 1993
doi: 10.1007/b98869. |
[11] |
S. Saavedra, D. B. Stouffer, B. Uzzi and J. Bascompte, Strong contributors to network persistence are the most vulnerable to extinction, Nature, 478 (2011), 233-235.
doi: 10.1038/nature10433. |
[12] |
H. L. Smith, Competing subcommunities of mutualists and a generalized Kamke theorem, SIAM J. Appl. Math., 46 (1986), 856-874.
doi: 10.1137/0146052. |
[13] |
G. Sugihara and H. Ye, Cooperative network dynamics, Nature (News and View), 458 (2009), 979-980.
doi: 10.1038/458979a. |
[14] |
Y. Takeuchi, Global Dynamical Properties of Lotka-Volterra Systems, World Scientific Publishing Co., Inc., River Edge, NJ, 1996.
doi: 10.1142/9789812830548. |
[15] |
Y. Wang and H. Wu, Dynamics of a cooperation-competition model for the WWW market, Physica A, 339 (2004), 609-620.
doi: 10.1016/j.physa.2004.03.067. |
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