Synchronization of coupled limit cycles

A unified approach for analyzing synchronization in coupled systems of autonomous differential equations is presented in this work. Through a careful analysis of the variational equation of the coupled system we establish a sufficient condition for synchronization in terms of the geometric properties of the local limit cycles and the coupling operator. This result applies to a large class of differential equation models in physics and biology. The stability analysis is complemented with a discussion of numerical simulations of a compartmental model of a neuron.Comment: Journal of Nonlinear Science, accepte

Preparation and anticoagulant activity of the phosphosulfomannan PI-88

A yeast-derived phosphomannan mixture was chemically sulfonated and the composition and structure of the product mixture was studied. This phosphosulfomannan mixture, PI-88, is currently under clinical evaluation as an anti-cancer agent. Analysis using capillary electrophoresis demonstrated that PI-88 was a multi-component mixture. Gel permeation chromatography provided four fractions of PI-88 that contained components which differed in size from disaccharide to hexasaccharide, and by degree of sulfation. These fractions were characterised by spectroscopic and chromatographic methods and the structure of PI-88 is that expected based On the structure of the phosphomannan starting material. The anticoagulant activity of these fractions was evaluated and the structural requirements for,activity are described. (C) 2002 Editions scientifiques et medicales Elsevier SAS. All rights reserved

Neural Synchronization at Tonic-to-Bursting Transitions

We studied the synchronous behavior of two electrically-coupled model neurons as a function of the coupling strength when the individual neurons are tuned to different activity patterns that ranged from tonic firing via chaotic activity to burst discharges. We observe asynchronous and various synchronous states such as out-of-phase, in-phase and almost in-phase chaotic synchronization. The highest variety of synchronous states occurs at the transition from tonic firing to chaos where the highest coupling strength is also needed for in-phase synchronization which is, essentially, facilitated towards the bursting range. This demonstrates that tuning of the neuron’s internal dynamics can have significant impact on the synchronous states especially at the physiologically relevant tonic-to-bursting transitions