Abstract and Applied Analysis

Nonhyperbolic Periodic Orbits of Vector Fields in the Plane Revisited

Denis de Carvalho Braga, Luis Fernando Mello, and Antonio Carlos Zambroni de Souza

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Abstract

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.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 212340, 19 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393449977

Digital Object Identifier
doi:10.1155/2013/212340

Mathematical Reviews number (MathSciNet)
MR3093767

Zentralblatt MATH identifier
1296.34075

Citation

Braga, Denis de Carvalho; Mello, Luis Fernando; Zambroni de Souza, Antonio Carlos. Nonhyperbolic Periodic Orbits of Vector Fields in the Plane Revisited. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 212340, 19 pages. doi:10.1155/2013/212340. https://projecteuclid.org/euclid.aaa/1393449977


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