Periodic phase-locking and phase slips in active rotator systems
File(s)
Working paper
Author(s)
Gandhi, P
Beaume, C
Knobloch, E
Type
Report
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.
Date Issued
2015-12-31
Copyright Statement
© 2015 The Authors
Identifier
http://arxiv.org/abs/1509.03582v1
Subjects
nlin.AO
Notes
37 pages, 22 figures