Mathematics Colloquia and Seminars

Return to Colloquia & Seminar listing

What input signals will lead to synchrony vs. desynchrony in a group of biological oscillators? This question connects with both classical dynamical systems analysis of entrainment and phase locking and with emerging studies of stimulation patterns for controlling neural network activity. We begin with the results of large-scale numerical optimization studies that seek to desynchronize a model of the Parkinsonian basal ganglia, and move to an analysis of a possible dynamical mechanism. Specifically, we focus our analysis on the response of a population of uncoupled, elliptically bursting neurons to a common pulsatile input. We extend a phase reduction from the literature to capture inputs of varied strength, leading to a circle map with discontinuities of various orders. This gives rise to response that either appear chaotic and desynchronized (with provably positive Lyaponov exponent), or periodic with a broad range of phase-locked periods. Throughout, we discuss the critical underlying mechanisms, including slow-passage effects through Hopf bifurcation, the role and origin of discontinuities, and the impact of noise.