title: Dynamics of weakly coupled parametrically forced oscillators.
abstract: The dynamics of two weakly coupled parametric oscillators are studied in the neighborhood of the primary subharmonic instability. The nature of both primary and secondary instabilities depends in a critical way on the permutation symmetries, if any, that remain after coupling is considered, and this depends on the relative phases of the parametric forcing terms. Detailed bifurcation sets, revealing a complex series of transitions organized in part by Bogdanov-Takens points, are calculated for representative sets of parameters. In the particular case of out-of-phase forcing the predictions of the coupled oscillator model are compared with direct numerical simulations and with recent experiments on modulated cross waves. Both the initial Hopf bifurcation and the subsequent saddle-node heteroclinic bifurcation are confirmed.
authors.affiliation: Escuela Técnica Superior de Ingeniería Aeronáutica y del Espacio, Universidad Politécnica de Madrid, Plaza de Cardenal Cisneros 3, 28040 Madrid, Spain.
authors.forename: P
authors.initials: P
authors.lastname: Salgado Sánchez
authors.affiliation: Escuela Técnica Superior de Ingeniería Aeronáutica y del Espacio, Universidad Politécnica de Madrid, Plaza de Cardenal Cisneros 3, 28040 Madrid, Spain.
authors.forename: J
authors.initials: J
authors.lastname: Porter
authors.affiliation: Escuela Técnica Superior de Ingeniería Aeronáutica y del Espacio, Universidad Politécnica de Madrid, Plaza de Cardenal Cisneros 3, 28040 Madrid, Spain.
authors.forename: I
authors.initials: I
authors.lastname: Tinao
authors.affiliation: Escuela Técnica Superior de Ingeniería Aeronáutica y del Espacio, Universidad Politécnica de Madrid, Plaza de Cardenal Cisneros 3, 28040 Madrid, Spain.
authors.forename: A
authors.initials: A
authors.lastname: Laverón-Simavilla