Gap bifurcations in nonlinear dynamical systems.
We investigate the dynamics generated by a type of equation which is common to a variety of physical systems where the undesirable effects of a number of self-consistent nonlinear forces are balanced by an externally imposed controlling harmonic force. We show that the equation presents a new sequence of bifurcations where periodic orbits are created and destroyed in such a nonsimultaneous way that may leave the appropriate phase-space occasionally empty of fundamental harmonic orbits and confined trajectories. A generic analytical model is developed and compared with a concrete physical example.
Rizzato
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Instituto de Física, Universidade Federal do Rio Grande do Sul, P.O.Box 15051, 91501-970, Porto Alegre, RS, Brasil. rizzato@if.ufrgs.br
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