Phase-locking dynamics of bi-directionally coupled electronic relaxation oscillators

We carry out experiments, analytical studies and numerical simulations of a system of two coupled comparator-based relaxation oscillators. We analytically obtain the parameter regime of stable n:1 phase-locked solutions. These regions in the parameter space are known as Arnold tongues. These Arnold tongues agree with our experimental observations. The dynamics of the variables is described by a system of differential equations, but with discontinuities at discrete times. Given that this characteristic makes the analysis challenging, an unusual approach was developed and used. This new approach can also be adopted to study other systems of coupled oscillators, making this article valuable to the scientific community.