We present detailed analytical and experimental results for a system of two comparator-based relaxation oscillators that are coupled via threshold modulation. Starting with the op-amp circuit equations, we derive parameter conditions that lead to n:1 phase-locked solutions, thereby obtaining predictions for the shapes of Arnold tongues for this system. These tongues are compared to experimental data and good agreement is found. We follow up with a stability analysis of phase-locked solutions. Specifically, we use two-timescale asymptotic analysis, and we check some results obtained therein against experimentally captured dynamics.

Behta, Emma, Guillermo H. Goldsztein, and L.Q. English. Phase-Locking Dynamics for Electronic Relaxation Oscillators via Threshold Pulse-Modulation: Comparing Experimental and Analytical Arnold Tongues. Physica D: Nonlinear Phenomena 454 (2023): e133849. https://www.sciencedirect.com/science/article/abs/pii/S0167278923002038

Lars English is a professor of Physics at Dickinson College.
Emma Behta, Dickinson College class of 2022.

For more information on the published version, visit Science Direct's Website. https://www.sciencedirect.com/science/article/abs/pii/S0167278923002038

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