Nonhyperbolic Periodic Orbits of Vector Fields in the Plane Revisited

作者:Braga Denis de Carvalho; Mello Luis Fernando*; Zambroni de Souza Antonio Carlos
来源:Abstract and Applied Analysis, 2013, 212340.
DOI:10.1155/2013/212340

摘要

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 Lienard-type equations and in Bazykin's predator-prey system.

  • 出版日期2013

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