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

TL;DR

This study investigates the synchronization behavior of a 555-IC based electronic oscillator system under strong coupling, revealing a degenerate bifurcation point where multiple phase-locking regions converge, supported by experiments and modeling.

Contribution

First experimental analysis of a 555-IC oscillator system in the strong coupling regime, identifying a unique bifurcation point and validating findings with a mathematical model.

Findings

Existence of a degenerate bifurcation point at NFF=2 in strong coupling

Convergence of phase-locking regions at the bifurcation point

Experimental and modeling results corroborate the bifurcation phenomenon

Abstract

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.