Multiple Focus and Hopf Bifurcations in a Predator-Prey System with Nonmonotonic Functional Response

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dc.contributor.authorXiao, Dongmei
dc.contributor.authorZhu, Huaiping
dc.date.accessioned2007-01-31T19:58:53Z
dc.date.available2007-01-31T19:58:53Z
dc.date.issued2006
dc.description.abstractIn this paper, we develop a criterion to calculate the multiplicity of a multiple focus for general predator prey systems. As applications of this criterion, we calculate the most multiplicity of a multiple focus in a predator prey system with nonmonotonic functional response p(x) = x/(ax^2+bx+1) studied by Zhu, Campbell and Wolkowicz [26] and prove that the degenerate Hopf bifurcation is of codimension two. Furthermore, we show that there exist parameter values for which this system has a unique positive hyperbolic stable equilibrium and exactly two limit cycles, the inner one is unstable and outer one is stable. Numerical simulations for the existence of the two limit cycles bifurcated from the multiple focus were also given in support of the criterion.
dc.format.extent270375 bytes
dc.format.mimetypeapplication/pdf
dc.identifier.citationD. Xiao and H. Zhu, ā€œMultiple Focus and Hopf Bifurcations in a Predator-Prey System with Nonmonotonic Functional Response,ā€ SIAM Journal on Applied Mathematics, vol. 66, no. 3, pp. 802ā€“819, Jan. 2006.
dc.identifier.issn0036-1399
dc.identifier.urihttp://hdl.handle.net/10315/903
dc.identifier.urihttps://doi.org/10.1137/050623449
dc.language.isoen
dc.publisherSIAM Journal on Applied Mathematics
dc.rightsCopyright Ā© 2006 Society for Industrial and Applied Mathematics
dc.subjectpredator prey
dc.subjectLiƩnard system
dc.subjectmultiple focus
dc.subjectHopf bifurcation
dc.subjectcodimension two
dc.subjectlimit cycles
dc.titleMultiple Focus and Hopf Bifurcations in a Predator-Prey System with Nonmonotonic Functional Response
dc.typeArticle

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