Dynamical Behavior of Two Coupled Two-Stroke Relaxation Oscillators

Abstract

Starting from [J.-M. Ginoux et al., Torus breakdown in a uni junction memristor, Int. J. Bifurcation Chaos 28(10) (2018) 1850128; J.-M. Ginoux et al., Torus breakdown in a two-stroke relaxation memristor, Chaos Solitons Fractals 153 (2021) 111594], we define a model which describes the dynamical behavior of a class of two-stroke oscillators (i.e., nonlinear oscillators with two distinct phases per cycle). We highlight some properties of the model still not taken into account, like presence of a global bifurcation and bistability for some regions of the parameters space. We then extend the model to study two coupled two-stroke oscillators, where synchrony and anti-synchrony regimes appear as well as transient chaos and intermittency phenomena. We finally compare the theoretical results on synchrony regimes with the corresponding experimental data obtained from a circuit where two relaxation oscillators, based on the Unijunction Transistor (UJT) electronic component, are coupled together. The comparison shows a good qualitative agreement between the experiments and the theoretical results.