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Passage through resonance and autoresonance in x(2n)-type potentials.

Resonant dynamics of a particle in an x(2n)-type potential driven by an oscillation with adiabatically varying frequency is investigated. It is shown that, under certain conditions, when the driving frequency increases in time and passes the resonance with the unperturbed system, the oscillator phase locks to the drive and, later, this phase locking is sustained, i.e., the system remains in autoresonance. The initial phase locking by passage through resonance is the main ingredient of the transition to autoresonance and comprises the generalization of previous results for nearly parabolic potentials.