A seminar at Center for Mathematical Sciences,

June 19 ，Friday， at 11:00am

Speaker：Deng Bo，University of Nebraska-Libcoln , USA

Time：2015年6月19日（星期五）上午11:00—12:00

Location：Center for Mathematical Sciences， Room 813（创新研究院恩明楼813室）

Title: Spike Renormalization: One Big Chaos

Abstract: In this talk we will consider the dynamics of bursting spikes from mechanistic neuronal models. It is known that the number of spikes per burst undergoes bifurcation from n to n+1 spikes as some small parameter converges to zero. We will demonstrate that the bifurcation sequence is subject to renormalization so that the bifurcation sequence is equivalent to an orbit of the renormalization operator in the space of one-dimensional maps containing the Poincare return map of the neuronal model around the bursting spikes. We will also demonstrate that this spike renormalization operator gives rise to a new universal number along the spike bifurcation sequence, and it is the first natural number 1. We will further demonstrate that the operator is chaotic and contains all finite dimensional systems.