[00436] Coupled dynamical systems: from data analysis to biomathematics
Session Time & Room : 2C (Aug.22, 13:20-15:00) @F308
Type : Proposal of Minisymposium
Abstract : This minisymposium presents recent results in the study of coupled systems, from small groups of elements (neurons, cardiomyocytes, chemical reactions, and so on) to large ones. We propose different lines of study from data analysis techniques to dynamical systems theory approaches to deal with these problems from isolated systems to coupled systems .
Organizer(s) : Roberto Barrio, Hiroyuki Kitajima, Valeriy Makarov, Ivan Tyukin
[03097] Fractal dimension of multidimensional biological recordings
Format : Talk at Waseda University
Author(s) :
Valeri A. Makarov (Universidad Complutense de Madrid)
Abstract : A linear mixture model can describe multisite LFPs, EEG, and MEG recordings. The fractal dimension (FD) of such multidimensional data can measure the complexity of different brain states. However, the local stationarity, the data's high dimension, and noise limit the assessment of FD from raw data. We discuss theoretical principles and methods derived from the model enabling accurate estimation of the FD, and illustrate them on synthetic and biological data.
[03895] Lyapunov-like characterization of ghost and weak attractors in complex dynamical systems
Format : Talk at Waseda University
Author(s) :
Ivan Y Tyukin (King's College London)
Alexander N Gorban (University of Leicester)
Roqaiah Alsolami (University of Leicester)
Tatiana Tyukina (University of Leicester)
Abstract : In this talk we discuss the problem of identifying and formally characterizing ghost and weak attractors in complex dynamical systems governed by systems of coupled nonlinear ordinary differential equations. We present a set of conditions enabling to determine if an equilibrium is a weak attractor in terms of the corresponding Jacobian and Hessian matrices. We show how these results can be used to constructively define and determine the existence of ghost attractors in such systems.
[03442] Flip-flip bifurcations in mathematical cardiac systems with and without symmetry
Format : Talk at Waseda University
Author(s) :
Hiroyuki Kitajima (Kagawa University)
Abstract : We study the intersection of double-flip (period-doubling) bifurcations in a parameter plane. We derive normal forms for discrete-time and continuous-time systems. Using these normal forms, we clarify the bifurcation structure around the flip-flip bifurcation point. We apply these analytical results to a system of coupled ventricular cell models. We make the simplest model for generating discordant alternans and clarify that two parameters play key roles in generating discordant alternans.
[03235] Generation of early afterdepolarizations in cardiomyocytes: Fast-slow and bifurcation analysis
Format : Talk at Waseda University
Author(s) :
Roberto Barrio (University of Zaragoza, Spain)
Jorge Jover-Galtier (University of Zaragoza)
M. Angeles Martinez (University of Zaragoza)
Lucia Perez (University of Oviedo)
Sergio Serrano (University of Zaragoza)
Esther Pueyo (University of Zaragoza)
Abstract : We analyze the dynamical mechanisms underlying the formation of arrhythmogenic early afterdepolarizations (EADs) in the cardiomyocyte models of Sato et al. (a biophysically detailed model of dimension 27) and Luo-Rudy (dimension 3). Based on a comparison of the two models, with detailed bifurcation analysis using continuation techniques and using a fast-slow decomposition in the simple model and numerical explorations in the complex model, we propose a conjectured scheme of the formation of EADs that fits well with electrophysiological experimental data on EAD generation.
