Synchronization regions of two pulse-coupled electronic piecewise linear oscillators

Stable synchronous states of different order were analytically, numerically and experimentally characterized in pulse-coupled light-controlled oscillators (LCOs). The Master-Slave (MS) configuration was studied in conditions where different time-scale parameters were tuned under varying coupling strength. Arnold tongues calculated analytically - based on the piecewise two-time-scale model for LCOs - and obtained numerically were consistent with experimental results. The analysis of the stability pattern and tongue shape for (1 : n) synchronization was based on the construction of return maps representing the Slave LCO evolution induced by the action of the Master LCO. The analysis of these maps showed that both tongue shape and stability pattern remained invariant. Considering the wide variation range of LCO parameters, the obtained results could have further applications on ethological models.