Abstract
I present dynamical mechanisms responsible for transition frequencies, which are hidden in the homoclinic (HC) to supercritical Andronov-Hopf (AH) bifurcation switching in the two-dimensional Hindmarsh-Rose (2DHR) oscillator. For this purpose, I derive frequency gradients with respect to the input current and timescale in the 2DHR oscillator. The frequency gradients are formulated with phase response curves (PRCs) by expanding the firing frequency with small perturbations of the input current and timescale on the one-dimensional phase space of the 2DHR oscillator. I thus find two different types of striking breaks in the frequency plot with respect to the timescale, the sigmoid functional frequency and the discontinuous frequency. I also show effects of the unique PRC change on these transition frequencies.
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