Frequency Gradient with Respect to Temperature for Determination of Classification of the Phase Response Curve

The interesting task here is to study the frequency-current (f–I) curve and phase response curve (PRC), subject to neural temperature variations, because the f–I curve and PRC are important measurements to understand dynamical mechanisms of generation of neural oscillations, and the neural temperature is widely known to significantly affect the oscillations. Nevertheless, little is discussed about how the temperature affects the f–I curve and PRC. In this study, frequencies of the neural oscillations, modulated with the temperature variations, are quantified with an average of the PRC. The frequency gradient with respect to temperature derived here gives clear classifications of the PRC, regardless of the form. It is also indicated that frequency decreases with an increase in temperature, resulted from bifurcation switching of the saddle-homoclinic to the saddle-node on an invariant circle.