Synchronization

and

emergent coordination

Satellite Conference

European Conference on Complex Systems

Dresden, October 4

Workshop organizers:

Ulrich Parlitz Michael Rosenblum

Universität Göttingen Universität Potsdam

Summary

The Workshop will gather researchers investigating collective dynamics in various fields of science, such as ecology, cardiovascular and brain dynamics, cell dynamics, physics, complex networks etc. The workshop will provide a unique opportunity for discussions and exchange of ideas between theoreticians and experimentalists working in this rapidly developing field.

Synchronization is found in many natural and man-made systems, from microscale (e.g., cells) to macroscale (ecological systems). The speakers of the Workshop will address a rather broad spectrum of synchronization phenomena in various disciplines, focus on the universal aspects of this nonlinear phenomenon and describe it from different perspectives.

In particular, synchronization of complex, multi-agent systems is a topic of high interest and currently attracts attention of many researchers, from pure mathematicians to physiologists. This interdisciplinary nature of the field calls for a meeting like this one, where purely theoretical talks will alternate with presentation of various applications and experiments. We believe that this broadness of interests of speakers will be useful both for experts and for scientists, who are not active in this field but nevertheless want to know the state of the art. Last not least, we hope that this Workshop will help to increase the existing and establish new cooperation between theoreticians and experimentalists.

Invited speaker

8:40 - 9:25
Marc Timme, Network Dynamics Group, Max Planck Institute for Dynamics & Self-Organization, Göttingen, Germany

"Which Network Connectivities Generate a Given Dynamics?"

Abstract: We present two alternative perspectives that may aid our understanding of structure-dynamics relations of complex networks.

First, can we design a network, e.g. by modifying the features of units or interactions, such that it exhibits a desired dynamics? Here we positively answer this question analytically for networks of spiking neural oscillators [1, 2], by finding the set of all networks that exhibit a given arbitrary periodic spike pattern as an invariant dynamics. The method covers networks of different types of neurons, excitatory and inhibitory couplings, and interaction delays that may be heterogeneously distributed. We illustrate the applicability of the method by designing networks that exhibit a predefined dynamics and simultaneously minimize the networks' wiring costs, i.e. are structurally optimal.
Second, we present a method to infer the connectivity of a given network from its stable response dynamics. For instance, the long-term stationary response of phase-coupled oscillators to temporally constant driving depends characteristically
on both the driving signals and the underlying network connectivity [3]. Thus, for a given driving condition, measuring the phase differences
and the collective frequency reveals information about how the units are interconnected. Sufficiently many repetitions for different driving
conditions yield the entire network connectivity from measuring the response dynamics only [4].

[1] R.-M. Memmesheimer and M. Timme, Phys. Rev. Lett. 97,188101 (2006).
[2] R.-M. Memmesheimer and M. Timme, Physica D 224,182 (2006).
[3] M. Timme, Europhys. Lett. 76, 367 (2006).
[4] M. Timme, Phys. Rev. Lett. 98, 224101 (2007).

Speakers

9:25 - 9:55
Bernd Blasius, University of Oldenburg, Germany

"Synchronization of cell cycles in a phytoplankton chemostat"

Abstract: We present experimental results for the dynamics of a single species phytoplankton population in a chemostat. In our experiments we observe small-amplitude oscillations of algal densities which can be induced by external perturbation of the system. The emergence of these oscillations can be understood due to synchronization of the algal cell cycles which are coupled by the density of the limiting nutrients. The experimental results agree very well to simulation results in a system of interacting cell-cycle oscillators.

9:55 - 10:25
Laura Cimponeriu, Potsdam University, Germany

"Phase models of coupled nonlinear oscillators from time series: methods and applications"

Abstract: My talk focuses on the usage of phase dynamics models in the study of interaction among observed oscillator systems. A novel approach for reconstructing an observable independent, invariant representation of the dynamics of coupled oscillators will be presented. The main issues addressed are: (1) reconciling theoretical phase dynamics models with observational data, (2) reconstructing invariant phase models from time series, and (3) inferring interaction properties (e.g., strength, directionality). We further illustrate how this novel approach can be used to uncover the interaction of coupled oscillators from experimental data. A version of the classical Huygens' pendulum clocks experiment is used as a demonstration.

11:00 - 11:30
Janusz Kozlowski , University of Szczecin, Poland

“Farey tree as an organizing relation between the stimulation and response frequencies in EEG photic driving”

Abstract: The results of the analysis of data obtained during Intermittent Photic Stimulation (IPS) with white light at thefrequencies from 6Hz to 33 Hz with 3 Hz steps and of 3 sec duration are discussed. There were 11 female subjects with a mean age 20 years (ranging from 15 to 25) examined. Among them there were 6 epileptic patients and 5 subjects with the response within the norm. The data were recorded in the Department of Neurology, Pomeranian Medical University in Szczecin, Poland. The samples of two-second duration of the EEG records for each stimulation frequency for each subject were transformed into power spectra using Fast Fourier Transformation. The peaks from power spectra were extracted for each subject for each stimulating frequency separately and then summed up. The results, plotted in the form of a function: response frequency vs. stimulating frequency, revealed a structure of synchronized states which was similar for healthy and epileptic subjects. The synchronized behavior observed during IPS can be described using a mathematical formula called the Farey tree. In general, the whole structure of the ratios between the two frequencies can be predicted using the Farey tree construction. This type of structure in the data obtained from the EEG was for the first time noticed and reported.

11:30 - 12:00
Jürgen Kurths, Potsdam University, Germany

"Structural and functional cluster of complex brain networks"

Abstract: Recent research has revealed a rich and complicated network topology in the cortical connectivity of mammalian brains. A challenging task is to understand the implications of such network structures on the functional organization of the brain activities. This is studied here basing on dynamical complex networks. We investigate synchronization
dynamics on the cortico-cortical network of the cat by modeling each node (cortical area) of the network with a sub-network of interacting excitable neurons. We find that the network displays clustered synchronization behaviour and the dynamical clusters coincide with the topological community structures observed in the anatomical network. Our results provide insights into the relationship between the global organization and the functional specialization of the brain cortex.

12:00 - 12:30 
Stefan Luther, Cornell/Max Planck Institute,  Germany

"Dynamics and Control of Phase Singularities in excitable media "

Abstract: Spatially extended excitable media like cardiac tissue exhibit defect (or phase singularity) mediated turbulence in terms of irregular wave fronts or turbulent spiral dynamics. In heart dynamics this spatio-temporal chaotic state corresponds to an electro-mechanical malfunction of the heart and may result in sudden cardiac death. Therefore, the control of these dynamical patterns is desirable. We shall present control methods for (locally) stabilizing and manipulating spatio-temporal chaos in excitable media and discuss synchronization phenomena caused by control.

2:00 - 2:30 
Arkady Pikovsky, Potsdam University, Germany

"Synchronization by common noise: application to neuron's reliability"

Abstract: We consider theoretically and numerically the effect of common noise on identical and nearly identical nonlinear oscillators and show that synchronization sets on provided the largest Lyapunov exponent is negative. We also demonstrate that sufficiently strong noise may lead to desynchronization. The relevance of this for noise-driven neurons is discussed.



2:30 - 3:00
Olga Sosnovtseva, Danish Technical University, Danmark

"Dynamics of glia regulatory and potassium signaling mechanisms in neuron-neuron communication"

Abstract: We propose a generalized mathematical model of the tripartite synapse that includes a presynaptic neuron, the synaptic terminal itself, a postsynaptic neuron, and a glial cell. The glial cell is assumed to be activated via two different pathways: (i) the fast increase of intercellular potassium concentration produced by the spiking activity of the postsynaptic neuron, and (ii) the slow production of a mediator triggered by the synaptic activity. Our model predicts the long-term potentiation of the postsynaptic neuron as well as various calcium transients in response to the activation of different pathways. With potassium considered to be a signaling messenger in extracellular the dual nature of the resource-mediated coupling is found to be responsible for the coexistence of competing patterns of in- and anti-phase synchronization between neuron. By comparison with conventional gap junctional coupling, potassium signaling gives rise to considerable changes of the cellular response to external stimuli. consider theoretically and numerically the effect of common noise on identical and nearly identical nonlinear oscillators and show that synchronization sets on provided the largest Lyapunov exponent is negative. We also demonstrate that sufficiently strong noise may lead to desynchronization. The relevance of this for noise-driven neurons is discussed.

3:00 - 3:30
Aneta Stefanovska, Lancaster University, UK

"What is peculiar to synchronization in living systems? Why the exchange of energy and matter cannot be neglected"

Abstract: We seek to characterise the effect on its dynamical properties of the continuous exchange of energy and matter between the cardiovascular system and its environment, placing particular emphasis on cardio-respiratory synchronization. Data from anaesthesia (with low exchange rate), rest (moderate exchange) and exercise (high exchange) will be considered. The continuous transition in the cardio-respiratory synchronization ratio detected in healthy subjects at rest will be discussed, together with the observed differences between states of high and low energy/matter exchange.

3:30 - 4:00
Serhiy Yanchuk, WIAS/Humboldt University, Berlin, Germany

"How size of a large system affects its dynamics?"

Abstract: We discuss generic destabilization phenomena, which occur in large systems of different kinds: delay-differential equations with large delay and large lattices of coupled time-continuous oscillators.

4:30 - 5:00
Ulrich Parlitz, University of Göttingen, Göttingen, Germany

"Analyzing and forecasting synchronized dynamics"

Abstract: Methods for detecting synchronization from time series are discussed und compared. Furthermore, different modeling methods are applied to predict the onset of synchronization and to forecast synchronized (mean field) dynamics of oscillator networks. All topics will be illustrated by numerical and experimental examples.

5:00 - 5:30
Michael Rosenblum, Potsdam University, Germany

"Self-Organized Quasiperiodicity in Oscillator Ensembles with Global Nonlinear Coupling"

Abstract: We describe a transition from fully synchronous periodic oscillations to partially synchronous quasiperiodic dynamics in ensembles of identical oscillators with all-to-all coupling that nonlinearly depends on the generalized order parameters. We present an analytically solvable model that predicts a regime where the mean field does not entrain individual oscillators, but has a frequency incommensurate to theirs. The self-organized onset of quasiperiodicity is illustrated with Landau-Stuart oscillators and a Josephson junction array with a nonlinear coupling.