Free Access
| Issue |
Math. Model. Nat. Phenom.
Volume 8, Number 5, 2013
Bifurcations
|
|
|---|---|---|
| Page(s) | 95 - 118 | |
| DOI | https://doi.org/10.1051/mmnp/20138507 | |
| Published online | 17 September 2013 | |
- J. F. Andrews. A mathematical model for the continuous culture of microorganisms utilizing inhibitory substrates. Biotechnol. Bioeng., 10 (1968), 707-723. [CrossRef] [Google Scholar]
- R. Bogdanov. Bifurcations of a limit cycle for a family of vector fields on the plane. Selecta Math. Soviet. 1 (1981), 373-388. [Google Scholar]
- R. Bogdanov. Versal deformations of a singular point on the plane in the case of zero eigen-values. Selecta Math. Soviet. 1 (1981), 389-421. [Google Scholar]
- F. Brauer. Periodic solutions of some ecological models. J. Theor. Biol. 69 (1977), 143-152. [CrossRef] [PubMed] [Google Scholar]
- F. Brauer, D. A Sánchez. Periodic environments and periodic harvesting. Natural Resource Modeling. 16(3) (2003), 233-244. [CrossRef] [Google Scholar]
- J. B. Collings. The effects of the functional response on the bifurcation behavior of a mite predator-prey interaction model. J. Math. Biol., 36 (1997), 149-168. [CrossRef] [Google Scholar]
- S.-N. Chow, J. K. Hale. Methods of Bifurcation Theory. Springer-Verlag, Berlin-Heidelberg-New York, 1982. [Google Scholar]
- R. M. Etoua, C. Rousseau. Bifurcation analysis of a Generalissed Gause model with prey harvesting and a generalized Holling response function of type III. J. Differential Equations, 249 (2010), 2316-2356. [CrossRef] [MathSciNet] [Google Scholar]
- M. W. Hirsch, S. Smale, R. L. Devaney. Differential Equations, Dynamical Systems and An Introduction to Chaos. Elsevier, California, 2004. [Google Scholar]
- E. Hammill, O. L. Petchey, B. R. Anholt. Predator functional response changed by induced defenses in prey. The American Naturalist, 176(6) (2010), 723-731. [CrossRef] [PubMed] [Google Scholar]
- Y. Lamontagne, C. Coutu, C. Rousseau. Bifurcation analysis of a predator-prey system with generalized Holling type III functional response. J. Dynam. Differential Equations. 20 (2008), 535-571. [Google Scholar]
- R. May, J. R. Beddington, C. W. Clark, S. J. Holt, R. M. Laws. Management of multispecies fisheries. Science, 205 (1979), 267-277. [CrossRef] [PubMed] [Google Scholar]
- L. Perko. Differential Equations and Dynamical Systems. Springer, New York, 1996. [Google Scholar]
- S. Ruan, D. Xiao. Global analysis in a predator-prey system with nonmonotonic functional response. SIAM J. Appl. Math., 61(4) (2001), 1445-1472. [CrossRef] [Google Scholar]
- F. Takens. Forced oscillations and bifurcation, in “Applications of Global Analysis I”. Comm. Math. Inst. Rijksuniversitat Utrecht. 3 (1974), 1-59. [Google Scholar]
- R. J. Taylor. Predation. Chapman and Hall, New York, 1984. [Google Scholar]
- G. S. K. Wolkowicz. Bifurcation analysis of a predator-prey system involving group defence. SIAM J. Appl. Math. 48 (1988), 592-606. [CrossRef] [MathSciNet] [Google Scholar]
- D. Xiao, H. Zhu. Multiple focus and hopf bifurcations in a predaotr-prey system with nonmonotonic functional response. SIAM J. Appl. Math. 66 (2006), 802-819. [CrossRef] [Google Scholar]
- H. Zhu, S. A. Campbell, G. S. K. Wolkowicz. Bifurcation analysis of a predator-prey system with nonmonotonic functional response. SIAM J. Appl. Math. 63 (2002), 636-682. [Google Scholar]
- Z. Zhang, T. Ding, W. Huang, Z. Dong. Qualitative Theory of Differential Equation. Transl. Math. Monogr. Vol. 101, Amer. Math. Soc. Providence, RI, 1992. [Google Scholar]
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