Nonhyperbolic Periodic Orbits of Vector Fields in the Plane Revisited | Zendy

Denis de Carvalho Braga | Zendy; Luis Fernando Mello | Zendy; Antônio Carlos Zambroni de Souza | Zendy

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Nonhyperbolic Periodic Orbits of Vector Fields in the Plane Revisited

Author(s) -

Denis de Carvalho Braga,

Luis Fernando Mello,

Antônio Carlos Zambroni de Souza

Publication year - 2013

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2013/212340

Subject(s) - mathematics , codimension , transversal (combinatorics) , periodic orbits , mathematical analysis , plane (geometry) , vector field , hopf bifurcation , bifurcation diagram , bifurcation theory , bifurcation , differential equation , pitchfork bifurcation , homoclinic bifurcation , geometry , nonlinear system , physics , quantum mechanics

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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