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2013 Nonhyperbolic Periodic Orbits of Vector Fields in the Plane Revisited
Denis de Carvalho Braga, Luis Fernando Mello, Antonio Carlos Zambroni de Souza
Abstr. Appl. Anal. 2013(SI18): 1-19 (2013). DOI: 10.1155/2013/212340


The main goal of this paper is to present a theory of approximation of periodic orbits of vector fields in the plane. From the theory developed here, it is possible to obtain an approximation to the curve of nonhyperbolic periodic orbits in the bifurcation diagram of a family of differential equations that has a transversal Hopf point of codimension two. Applications of the developed theory are made in Liénard-type equations and in Bazykin’s predator-prey system.


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Denis de Carvalho Braga. Luis Fernando Mello. Antonio Carlos Zambroni de Souza. "Nonhyperbolic Periodic Orbits of Vector Fields in the Plane Revisited." Abstr. Appl. Anal. 2013 (SI18) 1 - 19, 2013.


Published: 2013
First available in Project Euclid: 26 February 2014

zbMATH: 1296.34075
MathSciNet: MR3093767
Digital Object Identifier: 10.1155/2013/212340

Rights: Copyright © 2013 Hindawi

Vol.2013 • No. SI18 • 2013
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