title: Dynamics of phase slips in systems with time-periodic modulation.
abstract: The Adler equation with time-periodic frequency modulation is studied. A series of resonances between the period of the frequency modulation and the time scale for the generation of a phase slip is identified. The resulting parameter space structure is determined using a combination of numerical continuation, time simulations, and asymptotic methods. Regions with an integer number of phase slips per period are separated by regions with noninteger numbers of phase slips and include canard trajectories that drift along unstable equilibria. Both high- and low-frequency modulation is considered. An adiabatic description of the low-frequency modulation regime is found to be accurate over a large range of modulation periods.
authors.affiliation: Department of Physics, University of California, Berkeley, California 94720, USA.
authors.forename: Punit
authors.initials: P
authors.lastname: Gandhi
authors.affiliation: Department of Physics, University of California, Berkeley, California 94720, USA.
authors.forename: Edgar
authors.initials: E
authors.lastname: Knobloch
authors.affiliation: Department of Aeronautics, Imperial College London, London SW7 2AZ, United Kingdom.
authors.forename: Cédric
authors.initials: C
authors.lastname: Beaume