Dr. Rüdiger Thul: Complex patterns in networks of cardiac and neural oscillators
Dr. Rüdiger Thul (University of Nottingham):
“Complex patterns in networks of cardiac and neural oscillators”
Wednesday, 06.02.2019 at 2 pm (Munich city centre, Schellingstr. 4, Kleiner Physikhörsaal)
Networks are ubiquitous in the world around us and are at the heart of complex phenomena in the social, economic, engineering and natural sciences. Physics and biology are no exceptions to this, and I will begin with presenting modelling results on recently discovered microscopic cardiac alternans. This form of cardiac arrhythmia, which is a precursor to fatal cardiac pathologies such as sudden cardiac death, can be understood in terms of breaking synchrony in interacting intracellular signalling networks and the emergence of complex spatio-temporal patterns. Our analysis combines piecewise linear modelling (PWL) with the master stability function (MSF) approach, which allows us to perform the linear stability analysis semi-analytically. In particular, the MSF reduces the linear stability problem of the entire N node network to one of the same dimension as a single node, thus greatly facilitating the analysis. I will then apply the MSF technique to networks of non-smooth PWL neural oscillators, which have been a cornerstone for understanding brain dynamics. To deal with the non-smooth nature, I will introduce saltation matrices that describe the propagation of perturbations across the sites of discontinuities. Our results highlight that the common modelling practice of replacing steep nonlinearities with Heaviside step functions requires a rethinking of linear stability in some network dynamics. In all of the above cases, I will demonstrate that eigenvectors associated with the linear stability problem serve as excellent predictors of the emerging network state.