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Nonhyperbolic Periodic Orbits of Vector Fields in the Plane Revisited

Author

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  • Denis de Carvalho Braga
  • Luis Fernando Mello
  • Antonio Carlos Zambroni de Souza

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.

Suggested Citation

  • Denis de Carvalho Braga & Luis Fernando Mello & Antonio Carlos Zambroni de Souza, 2013. "Nonhyperbolic Periodic Orbits of Vector Fields in the Plane Revisited," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-19, August.
    • Handle: RePEc:hin:jnlaaa:212340
    DOI: 10.1155/2013/212340
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