中文  |  English
学术活动
当前位置 >> 首页 >> 学术活动 >> 2011
"Applications of dynamical systems in biology and synchronization" by Dr. Konstantinos Efstathiou (12月20日,周二,下午14:10—14:50)
发表时间:2011-12-20 阅读次数:1115次

 

Title: Applications of dynamical systems in biology and synchronization

 

Speaker: Konstantinos Efstathiou
                  Researcher, Department of Mathematics, University of Groningen, Netherlands

 

Time: 14:10 am—14:50am, December 20 (Tuesday)

 

Venue: Room 102, Sub-Building of East Guanghua Tower

 

Abstract:

The concept of synchronization plays a very important role in biology. I will present two systems that exhibit synchronization. The first such system is a network of pulse coupled oscillators with delay. Such networks are used for modelling, for example, the activity in biological neuron networks or the synchronization processes in networks of interacting agents. Because of the non-zero delay the state space of such systems is infinite dimensional. We study the existence of unstable attractors, i.e., of saddle periodic orbits whose stable set has non-empty interior. We prove that for any number of oscillators n >= 3 there is an open parameter region in which the system has unstable attractors. Moreover, in the case of n=4 oscillators we show that there exist unstable attractors with heteroclinic cycles between them. The second such system is a model for circadian rhythms. We study how a single pacer cell synchronizes to an periodic signal. This signal includes the effect of the external environment (light-dark cycle) but also the effect of the rest of the pacer cells. It turns out that such system can be described by a family of circle maps. We discuss the properties of this family (emphasizing resonances and Arnol’d tongues) and their biological significance.

版权所有 复旦大学计算系统生物学中心 技术支持:维程互联
地址:上海市邯郸路220号