### Inhalt des Dokuments

# Functional connectivity of distant cortical regions: role of remote synchronization and symmetry in interactions

Vesna Vuksanovic und Philipp Hövel

Functional MRI (fMRI) of ongoing brain activity at rest i.e. without any overt-directed behavior has revealed patterns of coherent activity, so called resting-state functional networks. The dynamical organization of nodes into these functional networks is closely related to the underlying structural connections. However, functional correlations have also been observed between cortical regions without apparent neural links, and mechanisms generating functional connectivity between distant cortical regions are largely unknown. It has been suggested that indirect connections and collective eects governed by network properties of the cortex play a signicant role. We use numerical simulations to investigate these mechanisms with reference to remote synchronization and network symmetry. Neural activity and the inferred hemodynamic response of the network nodes are modeled as sets of self-sustained oscillators, which are embedded in topologies of complex functional brain interactions. The coupling topology is based on connectivity maps derived from fMRI and DTI experiments. Consequently, our network model includes important information on whether direct or indirect neural connections exist between functionally associated regions. In the simulated functional networks, remote synchrony between pairs of nodes clearly arises from symmetry in the interactions, which are quantied by the number of shared neighbors. A larger joint neighborhood positively correlates with a higher level of synchrony. Therefore, our results indicate that a large overlapping neighborhood in complex networks of brain interactions gives rise to functional similarity between distant cortical regions.

Referenz:** **NeuroImage **97**, 1 (2014).

# When Nonlocal Coupling between Oscillators Becomes Stronger: Patched Synchrony or Multichimera States

Iryna Omelchenko, Oleh E. Omel’chenko, Philipp Hövel und Eckehard Schöll

Systems of nonlocally coupled oscillators can exhibit complex spatiotemporal patterns, called chimera states, which consist of coexisting domains of spatially coherent (synchronized) and incoherent dynamics.We report on a novel form of these states, found in a widely used model of a limit-cycle oscillator if one goes beyond the limit of weak coupling typical for phase oscillators. Then patches of synchronized dynamics appear within the incoherent domain giving rise to a multi-chimera state. We find that, depending on the coupling strength and range, different multichimera states arise in a transition from classical chimera states. The additional spatial modulation is due to strong coupling interaction and thus cannot be observed in simple phase-oscillator models.

Referenz: Phys. Rev. Lett. **110**, 224101 (2013).

# Experimental observation of chimeras in coupled-map lattices

Networks of nonlocally coupled phase oscillators can support chimera states in which identical oscillators evolve into distinct groups that exhibit coexisting synchronous and incoherent behaviours despite homogeneous coupling. Similar nonlocal coupling topologies implemented in networks of chaotic iterated maps also yield dynamical states exhibiting coexisting spatial domains of coherence and incoherence. In these discrete-time systems, the phase is not a continuous variable, so these states are generalized chimeras with respect to a broader notion of incoherence. Chimeras continue to be the subject of intense theoretical investigation, but have yet to be realized experimentally. Here we show that these chimaeras can be realized in experiments using a liquid-crystal spatial light modulator to achieve optical nonlinearity in a spatially extended iterated map system.We study the coherence incoherence transition that gives rise to these chimera states through experiment, theory and simulation.

Referenz: Nature Physics **8**, 658 (2012).

Siehe auch: Physics Today (vom 6. September 2012) und TU-Medieninformation.

# Loss of Coherence in Dynamical Networks: Spatial Chaos and Chimera States

Iryna Omelchenko, Yuri Maistrenko, Philipp Hövel und Eckehard Schöll

We discuss the breakdown of spatial coherence in networks of coupled oscillators with nonlocal interaction. By systematically analyzing the dependence of the spatio-temporal dynamics on the range and strength of coupling, we uncover a dynamical bifurcation scenario for the coherence-incoherence transition which starts with the appearance of narrow layers of incoherence occupying eventually the whole space. Our findings for coupled chaotic and periodic maps as well as for time-continuous Rössler systems reveal that intermediate, partially coherent states represent characteristic spatio-temporal patterns at the transition from coherence to incoherence.

Referenz: Phys. Rev. Lett. **106**, 234102 (2011)