Libro de Resúmenes / Book of Abstracts (Español/English)

Resumenes 176
⎧
2
dx ⎛ x ⎞ qx ⎧dx
⎛ x ⎞ qx
⎪ = r⎜1
− ⎟x
− y 4 ⎪ = r⎜1
− ⎟x
− y 4
⎪ dt ⎝ K ⎠ x + a ⎪ dt ⎝ K ⎠ x + a
⎪
⎪
X µ : ⎨
X µ : ⎨
⎪
2
⎪
⎪dy
⎛ px ⎞
=
⎪ ⎜ − c ⎟ y
⎪dy
⎛ px ⎞
=
4
⎩ dt ⎝ x + a ⎠
⎪ ⎜ − c ⎟ y
4
⎩ dt ⎝ x + a ⎠
parameters are all positives and have different biological meanings and
systems are analyzed at the first quadrant. It is proved that
1) (0,0) is always a saddle point meanwhile the nature of (K,0) dependent if
there exist equilibrium points at interior of the first quadrant.
2) There are conditions on the parameters for which it has two, one or none
positives equilibrium point.
3) When collapse the positives equilibrium point, this is a cusp point of
codimension 2 (Bogdanovic-Takens bifurcation)
4) There exist a region in the parameter space, where two limit cycles can
coexist.
Extinction of predators it is can possible when there are two positive
equilibrium points, because (K,0) is an atractor equilibrium point.
Referencias
[1] Aguilera-Moya, A. and González-Olivares, E, 2004, A Gause type model with
a generalized class of nonmonotonic functional response, In R. Mondaini
(Ed.) Proceedings of the Third Brazilian Symposium on Mathematical and
Computational Biology, E-Papers Servicos Editoriais Ltda, Río de Janeiro,
Vol. 2, 206-217.
[2] Collings, J. B., 1997, The effect of the functional response on the bifurcation
behavior of a mite predator-prey interaction model, Journal of Mathematical
Biology, 36.149-168.
[3] Freedman, H. I., 1980. Deterministic Mathematical Model in Population
Ecology. Marcel Dekker.
[4] Freedman, H. I., and Wolkowicz, G. S. W., 1986, Predator-prey systems with
group defence: The paradox of enrichment revisted, Bulletin of Mathematical
Biology Vol 8 No. 5/6, 493-508.
[5] González-Olivares, E. 2003. A predador-prey model with nonmonotonic
consumption function, In R. Mondaini (Ed.), Proceedings of the Second
Brazilian