PHASE INDEPENDENT RESETTING IN RELAXATION AND BURSTING OSCILLATORS

Relaxation oscillators that depend on one slow variable, such as the F itzhugh-Nagumo oscillator, reset in a phase-dependent manner. A comple te oscillation can be divided into two parts, the ''plateau'' and ''tr ough'', and a prematurely induced plateau or trough is significantly s horter than normal. The class of square-wave bursting oscillators can be viewed as relaxation oscillators with rapid spikes during the plate au, and reset similarly when modeled with one slow variable. However, it has been reported that a physiological bursting oscillator, the mem brane potential of the pancreatic beta-cell, resets in a phase-indepen dent manner, such that a prematurely induced plateau/trough has normal length. A possible model for such an oscillator requires two slow var iables, one to control the length of the plateau and the other the len gth of the trough. Here, we explore the geometric solution structure o f two such models, which exhibit the desired resetting. One is a gener alization of the Fitzhugh-Nagumo equations, and the other is a burstin g oscillator using known beta-cell electrical currents with an additio nal hypothetical slow outward current.