Excitation Waves on a Minimal Small-World Model

We examine traveling-wave solutions on a regular ring network with one additional long-range link that spans a distance d. The nodes obey the FitzHugh-Nagumo kinetics in the excitable regime. The additional shortcut induces a plethora of spatio-temporal behavior that is not present without it. We describe the underlying mechanisms for different types of patterns: propagation failure, period decreasing, bistability, shortcut blocking and period multiplication. For this purpose, we investigate the dependence on d, the network size, the coupling range in the original ring and the global coupling strength and present a phase diagram summarizing the different scenarios. Furthermore, we discuss the scaling behavior of the critical distance by analytical means and address the connection to spatially continuous excitable media.Comment: 14 pages, 11 figure

Dynamics of large-scale neuronal networks of the human cortex functional connectivity : From Twenty First Annual Computational Neuroscience Meeting: CNS*2012 Decatur, GA, USA. 21-26 July 2012

Published by BioMed Central Vuksanović, Vesna ; Hövel, Philipp : Dynamics of large-scale neuronal networks of the human cortex functional connectivity : From Twenty First Annual Computational Neuroscience Meeting: CNS*2012 Decatur, GA, USA. 21-26 July 2012. - In: BMC Neuroscience. - ISSN 1471-2202 (online). - 13 (2012), suppl. 1, P117. - doi:10.1186/1471-2202-13-S1-P117

Structural controllability of temporal networks

The control of complex systems is an ongoing challenge of complexity research. Recent advances using concepts of structural control deduce a wide range of control related properties from the network representation of complex systems. Here, we examine the controllability of systems for which the timescale of the dynamics we control and the timescale of changes in the network are comparable. We provide analytical and computational tools to study controllability based on temporal network characteristics. We apply these results to investigate the controllable subnetwork using a single input. For a generic class of model networks, we witness a phase transition depending upon the density of the interactions, describing the emergence of a giant controllable subspace. We show the existence of the two phases in real-world networks. Using randomization procedures, we find that the overall activity and the degree distribution of the underlying network are the main features influencing controllability.Bundesministerium für Bildung und Forschung 10.13039/501100002347German Academic Exchange Service 10.13039/501100001655Peer Reviewe

Clustered Chimera States in Systems of Type-I Excitability

Chimera is a fascinating phenomenon of coexisting synchronized and desynchronized behaviour that was discovered in networks of nonlocally coupled identical phase oscillators over ten years ago. Since then, chimeras were found in numerous theoretical and experimental studies and more recently in models of neuronal dynamics as well. In this work, we consider a generic model for a saddle-node bifurcation on a limit cycle representative for neural excitability type I. We obtain chimera states with multiple coherent regions (clustered chimeras/multi-chimeras) depending on the distance from the excitability threshold, the range of nonlocal coupling as well as the coupling strength. A detailed stability diagram for these chimera states as well as other interesting coexisting patterns like traveling waves are presented