Figure 1.

Parameterizing the PRC and the voltage shapes. (a) The voltage (top) and the PRC (bottom) of the HH model (thin lines) at an applied current of 10μA/cm² are taken as empirical models to construct parameterized and piecewise linear shapes (thick lines; displayed here for A′ = 0.567, B′ = −0.5, and W′ = 0.075) formulated using Eqs. 1 and 2. Parametrization of these curves allows for consideration of very general PRCs and voltage forms. (b) Comparing the interaction function and the growth function obtained from the full model (thin lines) and those obtained from piecewise linear approximations (thick lines). Fourier expansion approximations using first few modes to the H(φ) that is computed using the piecewise linear formulation are shown in dashes. The growth function, G(φ), is simply H(−φ) − H(φ), and its intersections are the phase-locked solutions of the coupled system. The negative slopes at the intersections indicate stability. The piecewise model and the Fourier approximation predicted the in-phase (φ = 0) and antiphase (φ = 1/2) states and their stability accurately. The stability of the other phase locked states is also accurately predicted.