We demonstrate emergence of a complex state in a homogeneous ensemble of globally coupled identical oscillators, reminiscent of chimera states in locally coupled oscillator lattices. In this regime some part of the ensemble forms a regularly evolving cluster, while all other units irregularly oscillate and remain asynchronous. We argue that chimera emerges because of effective bistability which dynamically appears in the originally monostable system due to internal delayed feedback in individual units. Additionally, we present two examples of chimeras in bistable systems with frequency-dependent phase shift in the global coupling. [3]. In addition to the well-studied self-synchronization transition, of particular recent interest are complex states between synchrony and asynchrony [4]. On the other hand, a lot of attention have attracted regimes of coexistence of coherence and incoherence in oscillators lattices [5]. These states, also known as "chimeras", have been addressed in numerous theoretical studies [6] and demonstrated in an experiment [7]. Furthermore, it has been shown that already two interacting populations of globally coupled identical oscillators can for some initial conditions exhibit symmetry breaking of synchrony, so that one population synchronizes whereas the other remains asynchronous [8]; existence of such chimeras has been also confirmed experimentally [9]. A natural question, addressed in this Letter, is under which conditions can such a symmetrybreaking into synchronous and asynchronous groups be observed in a completely homogeneous globally coupled population of identical oscillators.In case of global coupling all oscillators are subject to the same force. Therefore, if the units are identical, one may expect that they should evolve similarly. This expectation is rather natural and is indeed true for simple systems like the standard Kuramoto model as well as for many other examples from the literature. However, in a system of identical globally coupled chaotic maps, K. Kaneko observed one large synchronized cluster and a cloud of scattered units (see Fig 2b in [10]) -a state reminiscent of a chimera. For periodic units such a state has been reported by Schmidt et al. [11], who studied nonlinearly coupled Stuart-Landau oscillators, see also [12]. These observations of identical nonlinear elements behaving differently in spite of being driven by the same force, indicate presence of bi-or multistability. Here we demonstrate that chimera-like states naturally appear for a minimal generalization of the popular Kuramoto-Sakaguchi phase model to the case of globally coupled identical phase oscillators with internal delayed feedback, and discuss the underlying mechanism of dynamically sustained bistability.Globally coupled self-sustained oscillators can be quite generally treated in the phase approximation [2]. In the simplest case of identical sine-coupled units such an ensemble of N units is described by the KuramotoSakaguchi model [13]:where ϕ are the oscillators' phases, ε > 0 is the coupli...

Internal signals like one's heartbeats are centrally processed via specific pathways and both their neural representations as well as their conscious perception (interoception) provide key information for many cognitive processes. Recent empirical findings propose that neural processes in the insular cortex, which are related to bodily signals, might constitute a neurophysiological mechanism for the encoding of duration. Nevertheless, the exact nature of such a proposed relationship remains unclear. We aimed to address this question by searching for the effects of cardiac rhythm on time perception by the use of a duration reproduction paradigm. Time intervals used were of 0.5, 2, 3, 7, 10, 14, 25, and 40 s length. In a framework of synchronization hypothesis, measures of phase locking between the cardiac cycle and start/stop signals of the reproduction task were calculated to quantify this relationship. The main result is that marginally significant synchronization indices (SIs) between the heart cycle and the time reproduction responses for the time intervals of 2, 3, 10, 14, and 25 s length were obtained, while results were not significant for durations of 0.5, 7, and 40 s length. On the single participant level, several subjects exhibited some synchrony between the heart cycle and the time reproduction responses, most pronounced for the time interval of 25 s (8 out of 23 participants for 20% quantile). Better time reproduction accuracy was not related with larger degree of phase locking, but with greater vagal control of the heart. A higher interoceptive sensitivity (IS) was associated with a higher synchronization index (SI) for the 2 s time interval only. We conclude that information obtained from the cardiac cycle is relevant for the encoding and reproduction of time in the time span of 2–25 s. Sympathovagal tone as well as interoceptive processes mediate the accuracy of time estimation.

With increasing age cognitive performance slows down. This includes cognitive processes essential for motor performance. Additionally, performance of motor tasks becomes less accurate. The objective of the present study was to identify general neural correlates underlying age-related behavioral slowing and the reduction in motor task accuracy. To this end, we continuously recorded EEG activity from 18 younger and 24 older right-handed healthy participants while they were performing a simple finger tapping task. We analyzed the EEG records with respect to local changes in amplitude (power spectrum) as well as phase locking between the two age groups. We found differences between younger and older subjects in the amplitude of post-movement synchronization in the β band of the sensory-motor and medial prefrontal cortex (mPFC). This post-movement β amplitude was significantly reduced in older subjects. Moreover, it positively correlated with the accuracy with which subjects performed the motor task at the electrode FCz, which detects activity of the mPFC and the supplementary motor area. In contrast, we found no correlation between the accurate timing of local neural activity, i.e. phase locking in the δ-θ frequency band, with the reaction and movement time or the accuracy with which the motor task was performed. Our results show that only post-movement β amplitude and not δ-θ phase locking is involved in the control of movement accuracy. The decreased post-movement β amplitude in the mPFC of older subjects hints at an impaired deactivation of this area, which may affect the cognitive control of stimulus-induced motor tasks and thereby motor output.

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Background:The interaction of different brain regions is supported by transient synchronization between neural oscillations at different frequencies. Different measures based on synchronization theory are used to assess the strength of the interactions from experimental data. One method of estimating the effective connectivity between brain regions, within the framework of the theory of weakly coupled phase oscillators, was implemented in Dynamic Causal Modelling (DCM) for phase coupling (Penny et al., 2009). However, the results of such an approach strongly depend on the observables used to reconstruct the equations (Kralemann et al., 2008). In particular, an asymmetric distribution of the observables could result in a false estimation of the effective connectivity between the network nodes.New method:In this work we built a new modelling part into DCM for phase coupling, and extended it with a distortion function that accommodates departures from purely sinusoidal oscillations.Results:By analysing numerically generated data sets with an asymmetric phase distribution, we demonstrated that the extended DCM for phase coupling with the additional modelling component, correctly estimates the coupling functions.Comparison with existing methods:The new method allows for different intrinsic frequencies among coupled neuronal populations and provides results that do not depend on the distribution of the observables.Conclusions:The proposed method can be used to analyse effective connectivity between brain regions within and between different frequency bands, to characterize m:n phase coupling, and to unravel underlying mechanisms of the transient synchronization.