Periodic forcing of a 555-IC based electronic oscillator in the strong coupling limit

We designed and developed a master-slave electronic oscillatory system (based on the 555-timer IC working in the astable mode), and investigated its dynamic behavior regarding synchronization. For that purpose we measured the rotation numbers corresponding to the phase-locking rhythms achieved in a large set of values of the normalized forcing frequency (NFF) and of the coupling strength between the master and the slave oscillators. In particular we were interested in the system behavior in the strong-coupling limit, because such problem has not been extensively studied from an experimental perspective. Our results indicate that, in such a limit, a degenerate codimension-2 bifurcation point at NFF=2 exists, in which all the phase-locking regions converge. These findings were corroborated by means of a mathematical model developed to that end, as well as by ad hoc further experiments.Comment: 12 pages, 11 figures, In Press in the International Journal of Bifurcation and Chao