What is the functional significance of generating a burst of spikes, as opposed to a single
spike? A dominant point of view is that bursts are needed to increase the reliability of …

Complex assemblies of interacting proteins carry out most of the interesting jobs in a cell,
such as metabolism, DNA synthesis, movement and information processing. These …

This book aims to provide an introduction to dynamical systems with multiple time scales. As
in any overview book, several topics are covered only quite briefly. My aim was to focus on …

Fifteen years have elapsed after the second edition of Practical Bifurcation and Stability
Analysis was published. During that time period the? eld of computational bifurcation has …

This book is based on a two-semester course in ordinary differential equations that I have
taught to graduate students for two decades at the University of Missouri. The scope of the …

We study the influence of coupling strength and network topology on synchronization
behavior in pulse-coupled networks of bursting Hindmarsh-Rose neurons. Surprisingly, we …

The aim of this paper is to explain critical features of the human primary generalized
epilepsies by investigating the dynamical bifurcations of a nonlinear model of the brain's …

Synchronization, in which individual dynamical units keep in pace with each other in a
decentralized fashion, depends both on the dynamical units and on the properties of the …

In this paper, the transitions of burst synchronization are explored in a neuronal network
consisting of subnetworks. The studied network is composed of electrically coupled bursting …

Mathematical biology is in the moment a prosperous and exciting field. New experimental
methods require more and refined models. While experimental data of traditional …