title: Tilted excitation implies odd periodic resonances.
abstract: Our aim is to unveil how resonances of parametric systems are affected when symmetry is broken. We showed numerically and experimentally that odd resonances indeed come about when the pendulum is excited along a tilted direction. Applying the Melnikov subharmonic function, we not only determined analytically the loci of saddle-node bifurcations delimiting resonance regions in parameter space but also explained these observations by demonstrating that, under the Melnikov method point of view, odd resonances arise due to an extra torque that appears in the asymmetric case.
authors: Instituto de Física "Gleb Wataghin," Universidade Estadual de Campinas, 13083-859 Campinas, SP, Brazil.|Instituto de Física da Universidade de São Paulo, 05315-970 São Paulo, SP, Brazil.
authors: G I
authors: GI
authors: Depetri
authors: Instituto de Física da Universidade de São Paulo, 05315-970 São Paulo, SP, Brazil.
authors: J C
authors: JC
authors: Sartorelli
authors: Instituto de Física da Universidade de São Paulo, 05315-970 São Paulo, SP, Brazil.|Department of Neuroscience, Physiology and Pharmacology, University College London, Gower Street, London WC1E 6BT, United Kingdom.
authors: B
authors: B
authors: Marin
authors: Institute for Complex Systems and Mathematical Biology, SUPA, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom.
authors: M S
authors: MS
authors: Baptista