Rapid convergence of time-averaged frequency in phase synchronized systems

Numerical and experimental evidence is presented to show that many phase synchronized systems of non-identical chaotic oscillators, where the chaotic state is reached through a period-doubling cascade, show rapid convergence of the time-averaged frequency. The speed of convergence toward the natural frequency scales as the inverse of the measurement period. The results also suggest an explanation for why such chaotic oscillators can be phase synchronized.Comment: 6 pages, 9 figure

Interoperable atlases of the human brain

International audienceThe last two decades have seen an unprecedented development of human brain mapping approaches at various spatial and temporal scales. Together, these have provided a large fundus of information on many different as-pects of the human brain including micro-and macrostructural segregation, regional specialization of function, connectivity, and temporal dynamics. Atlases are central in order to integrate such diverse information in a topo-graphically meaningful way. It is noteworthy, that the brain mapping field has been developed along several major lines such as structure vs. function, postmortem vs. in vivo, individual features of the brain vs. population-based aspects, or slow vs. fast dynamics. In order to understand human brain organization, however, it seems inevitable that these different lines are integrated and combined into a multimodal human brain model. To this aim, we held a workshop to determine the constraints of a multi-modal human brain model that are needed to enable (i) an integration of different spatial and temporal scales and data modalities into a common reference system, and (ii) efficient data exchange and analysis. As detailed in this report, to arrive at fully interoperable atlases of the human brain will still require much work at the frontiers of data acquisition, analysis, and represen-tation. Among them, the latter may provide the most challenging task, in particular when it comes to representing features of vastly different scales of space, time and abstraction. The potential benefits of such endeavor, however, clearly outweigh the problems, as only such kind of multi-modal human brain atlas may provide a starting point from which the complex relationships between structure, function, and connectivity may be explored

Synchronization control of interacting oscillatory ensembles by mixed nonlinear delayed feedback.

We propose a method for the control of synchronization in two oscillator populations interacting according to a drive-response coupling scheme. The response ensemble of oscillators, which gets synchronized because of a strong forcing by the intrinsically synchronized driving ensemble, is controlled by mixed nonlinear delayed feedback. The stimulation signal is constructed from the mixed macroscopic activities of both ensembles. We show that the suggested method can effectively decouple the interacting ensembles from each other, where the natural desynchronous dynamics can be recovered in a demand-controlled way either in the stimulated ensemble, or, intriguingly, in both stimulated and not stimulated populations. We discuss possible therapeutic applications in the context of the control of abnormal brain synchrony in loops of affected neuronal populations

Chimera states induced by spatially modulated delayed feedback.

Recently, we have presented spatially modulated delayed feedback as a novel mechanism, which generically generates chimera states, remarkable spatiotemporal patterns in which coherence coexists with incoherence [O. E. Omel'chenko et al., Phys. Rev. Lett. 100, 044105 (2008)]. Remarkably, such chimera states serve as a natural link between completely coherent states and completely incoherent states. So far, we have studied this mechanism with a self-consistency-based numerical analysis only. In contrast, in this paper we perform a thorough dynamical description and, in particular, a stability analysis of the emerging chimera states. For this, we apply a recently developed reduction procedure [A. Pikovsky and M. Rosenblum, Phys. Rev. Lett. 101, 264103 (2008)]. By combining analytical and numerical approaches, we systematically describe the relationship between the parameters of the delayed feedback on one hand and the properties of the chimera states on the other hand. We provide the general rules for an effective control and manipulation of the chimera states

Phase-locking swallows in coupled oscillators with delayed feedback.

We show that a nonlinear coupling with delayed feedback between two limit-cycle oscillators can lead to phase-locked, periodically modulated, and chaotic phase synchronization as well as to desynchronization. Parameter regions with stable phase-locked states attain the well-known form of the swallows or shrimps found and studied for nonlinear maps. We demonstrate that the swallow regions can be accompanied by a different bifurcation scenario where the periodic orbits of the phase-locked states undergo a torus bifurcation instead of a previously reported period-doubling bifurcation. This property has an impact on the spatial organization of the swallows in the parameter space. The swallow regions contribute to the synchronization domain of the considered system, and we analytically approximate the parameter synchronization threshold

Anti-kindling achieved by stimulation targeting slow synaptic dynamics.

Different stimulation techniques are introduced which specifically modulate the slow synaptic dynamics in a neuronal network model of the subthalamic nucleus with activity dependent synaptic plasticity.A modeling approach is utilized to investigate the effects of the different stimulation techniques. In particular, the short-term and long-term outcome is studied in a mathematical model for a population of bursting STN neurons subject to synaptic plasticity with symmetric spike timing characteristics. In our mathematical model in the absence of stimulation synchronized network states with strong connectivity (modeling disease states) as well as desynchronized states with weak connectivity (modeling healthy states) are stable.We demonstrate that different stimulation techniques induce an anti-kindling by shifting the target population to a weakly connected, desynchronized state. Intriguingly, long-term anti-kindling can even be achieved although during stimulus delivery the neuronal synchrony hardly decreases or even slightly increases. The therapeutic index and the impact of inhibition, calculated to compare the different stimulation techniques, indicate that coordinated rest stimulation might be particularly robust and reliable.The presented stimulation strategies and the results of our modeling study might have strong implications in the context of deep brain stimulation

Macroscopic entrainment of periodically forced oscillatory ensembles.

Large-amplitude oscillations of macroscopic neuronal signals, such as local field potentials and electroencephalography or magnetoencephalography signals, are commonly considered as being generated by a population of mutually synchronized neurons. In a computational study in generic networks of phase oscillators and bursting neurons, however, we show that this common belief may be wrong if the neuronal population receives an external rhythmic input. The latter may stem from another neuronal population or an external, e.g., sensory or electrical, source. In that case the population field potential may be entrained by the rhythmic input, whereas the individual neurons are phase desynchronized both mutually and with their field potential. Intriguingly, the corresponding large-amplitude oscillations of the population mean field are generated by pairwise desynchronized neurons oscillating at frequencies shifted far away from the frequency of the macroscopic field potential

Periodic patterns in a ring of delay-coupled oscillators.

We describe the appearance and stability of spatiotemporal periodic patterns (rotating waves) in unidirectional rings of coupled oscillators with delayed couplings. We show how delays in the coupling lead to the splitting of each rotating wave into several new ones. The appearance of rotating waves is mediated by the Hopf bifurcations of the symmetric equilibrium. We also conclude that the coupling delays can be effectively replaced by increasing the number of oscillators in the chain. The phenomena are shown for the Stuart-Landau oscillators as well as for the coupled FitzHugh-Nagumo systems modeling an ensemble of spiking neurons interacting via excitatory chemical synapses