Brain-Mind workshop at Fudan University

2012-01-02

On December 19-20, 2011 the Brain-Mind workshop took place at Fudan University in Shanghai. In the workshop I presented one of the invited keynotes. The title of my talk was “Applications of dynamical systems in biology and synchronization”.

The concept of synchronization plays a very important role in biology. In the talk I presented 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. Important questions here are the existence of unstable attractors, i.e., of saddle periodic orbits whose stable set has non-empty interior. In an earlier work we showed that for any number \(n\) of oscillators with \(n \ge 3\) there is an open parameter region in which the system has unstable attractors. Moreover, in the case of \(n = 4\) oscillators we showed that there exist unstable attractors with heteroclinic cycles between them. The second such system is a model for circadian rhythms. We have studied how a single pacer cell synchronizes to a 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. In the presentation I discussed the properties of this family (emphasizing resonances and Arnol’d tongues) and their biological significance.

Pacer cell response

2011-10-14

Recently Domien Beersma, Henk Broer, Kim Gargar, Igor Hoveijn, and I published in Physica D a paper on synchronization and circadian rhythms. The basic idea behind the paper is to study in a simple model how a single pacer cell synchronizes to a 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. In the paper we discuss the properties of this family (emphasizing resonances and Arnol’d tongues) and their biological significance.

Visiting Padova (again)

2011-01-14

Between 14 and 20 January 2011 I am visiting Andrea Giacobbe and Francesco Fassò at the Mathematics department in Padova to continue the work we did during my previous visit.

Resonance and synchronization

2011-01-14

On 31 January and 1 February 2011, Henk Broer, Xia Liu, and I, organize a workshop with subject Resonance and Synchronization. The purpose of the workshop is to explore the interaction between these two dynamical concepts and their applications in biological and mechanical systems. More information about the workshop including information about registration and about the program is available on the workshop’s website.

2010 review

2011-01-12

2010 has proved a pivotal year for me as I was elected to an assistant professor position. Besides that, I continued working on research problems on dynamical systems and the geometry of integrable Hamiltonian fibrations. Here is a short list of other 2010 events.

  • Four papers, finished in the previous year, were published in 2010. Two more papers, one on a covering spaces approach to fractional Hamiltonian monodromy and the other on circadian rhythms, were finished and are now under review.

  • Started a collaboration with Andrea Giacobbe which in 2010 brought Andrea once to Groningen and me once to Padova.

  • Gave 3 invited workshop talks (in Dijon, Santa Marinella, and Groningen) and two seminar talks (in Padova and Groningen).

  • Taught a course on Metric and Topological Spaces and gave the exercise sessions (werkcolleges) for the course of Analysis on Manifolds.

  • Attended the Lorentz Center workshop on Symplectic techniques in conservative dynamics.

  • Refereed 3 papers.

Furthermore, I did some programming, mostly improving old stuff. One new thing that I developed this year, was a web app where my coauthors and I can upload successive versions of the TeX files for our papers. This way it is possible to keep track of the changes that are introduced by different authors and to easily merge such changes.

Finally, I visited some very beautiful places (Iceland, Rome, Ireland) and, frustrated by the low-light performance of my Canon G9, I started using a Nikon D5000.