Periodic Solutions and Global Bifurcations for Nerve Impulse Equations

Abstract

Software for the Apple Macintosh microcomputer has been developed using the harmonic balance method for the detection of periodic solutions of feedback systems. This software, based on graphical criteria, also provides a good notion of the system’s dynamics and the way bifurcations occur, as well as the stability characteristics of the limit cycles. Here we report the results of its application to the FitzHugh equations for the nerve impulse. We numerically detect periodic solutions and global bifurcation points that, although theoretically predicted, had never been located. We describe amplitude, frequency and stability characteristics for these solutions, as well as the type and location of the bifurcation points.