Desynchronized State Research Articles

Time and ADHD in Danish Families: Mutual Affect Through Rhythm

ABSTRACT Based on fieldwork in Danish families living with ADHD, we expand on Nielsen’s insight that ADHD is experienced as a state of desynchronization by showing how family members’ rhythms mutually affect each other. We argue that ADHD is not only a biological and psychiatric condition, but also a temporal and socially responsive phenomenon. The intensity of ADHD is influenced by mutual affect in families and by general life circumstances. Families constitute bodily networks through which sensations, moods, rhythms, and practices spread and are passed down through generations. Yet, families use various time work strategies to manage rhythm affect.

Coordinated reset stimulation of plastic neural networks with spatially dependent synaptic connections.

Abnormal neuronal synchrony is associated with several neurological disorders, including Parkinson's disease (PD), essential tremor, dystonia, and epilepsy. Coordinated reset (CR) stimulation was developed computationally to counteract abnormal neuronal synchrony. During CR stimulation, phase-shifted stimuli are delivered to multiple stimulation sites. Computational studies in plastic neural networks reported that CR stimulation drove the networks into an attractor of a stable desynchronized state by down-regulating synaptic connections, which led to long-lasting desynchronization effects that outlasted stimulation. Later, corresponding long-lasting desynchronization and therapeutic effects were found in animal models of PD and PD patients. To date, it is unclear how spatially dependent synaptic connections, as typically observed in the brain, shape CR-induced synaptic downregulation and long-lasting effects. We performed numerical simulations of networks of leaky integrate-and-fire neurons with spike-timing-dependent plasticity and spatially dependent synaptic connections to study and further improve acute and long-term responses to CR stimulation. The characteristic length scale of synaptic connections relative to the distance between stimulation sites plays a key role in CR parameter adjustment. In networks with short synaptic length scales, a substantial synaptic downregulation can be achieved by selecting appropriate stimulus-related parameters, such as the stimulus amplitude and shape, regardless of the employed spatiotemporal pattern of stimulus deliveries. Complex stimulus shapes can induce local connectivity patterns in the vicinity of the stimulation sites. In contrast, in networks with longer synaptic length scales, the spatiotemporal sequence of stimulus deliveries is of major importance for synaptic downregulation. In particular, rapid shuffling of the stimulus sequence is advantageous for synaptic downregulation. Our results suggest that CR stimulation parameters can be adjusted to synaptic connectivity to further improve the long-lasting effects. Furthermore, shuffling of CR sequences is advantageous for long-lasting desynchronization effects. Our work provides important hypotheses on CR parameter selection for future preclinical and clinical studies.

Marmosets mutually compensate for differences in rhythms when coordinating vigilance.

Synchronization is widespread in animals, and studies have often emphasized how this seemingly complex phenomenon can emerge from very simple rules. However, the amount of flexibility and control that animals might have over synchronization properties, such as the strength of coupling, remains underexplored. Here, we studied how pairs of marmoset monkeys coordinated vigilance while feeding. By modeling them as coupled oscillators, we noted that (1) individual marmosets do not show perfect periodicity in vigilance behaviors, (2) nevertheless, marmoset pairs started to take turns being vigilant over time, a case of anti-phase synchrony, (3) marmosets could couple flexibly; the coupling strength varied with every new joint feeding bout, and (4) marmosets could control the coupling strength; dyads showed increased coupling if they began in a more desynchronized state. Such flexibility and control over synchronization require more than simple interaction rules. Minimally, animals must estimate the current degree of asynchrony and adjust their behavior accordingly. Moreover, the fact that each marmoset is inherently non-periodic adds to the cognitive demand. Overall, our study provides a mathematical framework to investigate the cognitive demands involved in coordinating behaviors in animals, regardless of whether individual behaviors are rhythmic or not.

Collective dynamics of coupled Lorenz oscillators near the Hopf boundary: Intermittency and chimera states.

We study collective dynamics of networks of mutually coupled identical Lorenz oscillators near a subcritical Hopf bifurcation. Such systems exhibit induced multistable behavior with interesting spatiotemporal dynamics including synchronization, desynchronization, and chimera states. For analysis, we first consider a ring topology with nearest-neighbor coupling and find that the system may exhibit intermittent behavior due to the complex basin structures and dynamical frustration, where temporal dynamics of the oscillators in the ensemble switches between different attractors. Consequently, different oscillators may show a dynamics that is intermittently synchronized (or desynchronized), giving rise to intermittent chimera states. The behavior of the intermittent laminar phases is characterized by the characteristic time spent in the synchronization manifold, which decays as a power law. Such intermittent dynamics is quite general and is also observed in an ensemble of a large number of oscillators arranged in variety of network topologies including nonlocal, scale-free, random, and small-world networks.

Memristive field effect in a single and multilayer neural network with different connection topologies

The network connectivities play an important role in displaying the vastly different collective dynamics in many complex systems. To demonstrate the presence of different dynamical states and their transition, we consider Hindmarsh-Rose neurons, which are linked up by electromagnetic interactions. The dynamical behaviors of the proposed system are specifically explored under three distinct network connectivities: Regular(RG), small-world (SW), and random (RAND) interactions. We discover that increasing coupling intensity illustrates the dynamical transition from the desynchronization state to the traveling wave state for all the considered network interactions. Particularly, the regular network shows the emergence of spatial symmetric patterns that transit to a homogeneous steady state while increasing the strength of magnetic field interaction. In addition, the transition from an asymmetric pattern to an in-homogeneous steady state is noticed for small-world and random networks. The investigation is then extended to a three-layer multiplex network in which nodes interact electromagnetically within (intra-) layers and magnetically between (inter-) layers, since many complex networks in the real world have large numbers of nodes organized (or located) in different subnetworks. We show that increasing the coupling intensity leads to synchronization in all layers and, eventually, a rest state at high coupling strength.

Disturbance of the Circadian System in Shift Work and Its Health Impact

The various non-standard schedules required of shift workers force abrupt changes in the timing of sleep and light-dark exposure. These changes result in disturbances of the endogenous circadian system and its misalignment with the environment. Simulated night-shift experiments and field-based studies with shift workers both indicate that the circadian system is resistant to adaptation from a day- to a night-oriented schedule, as determined by a lack of substantial phase shifts over multiple days in centrally controlled rhythms, such as those of melatonin and cortisol. There is evidence that disruption of the circadian system caused by night-shift work results not only in a misalignment between the circadian system and the external light-dark cycle, but also in a state of internal desynchronization between various levels of the circadian system. This is the case between rhythms controlled by the central circadian pacemaker and clock genes expression in tissues such as peripheral blood mononuclear cells, hair follicle cells, and oral mucosa cells. The disruptive effects of atypical work schedules extend beyond the expression profile of canonical circadian clock genes and affects other transcripts of the human genome. In general, after several days of living at night, most rhythmic transcripts in the human genome remain adjusted to a day-oriented schedule, with dampened group amplitudes. In contrast to circadian clock genes and rhythmic transcripts, metabolomics studies revealed that most metabolites shift by several hours when working nights, thus leading to their misalignment with the circadian system. Altogether, these circadian and sleep-wake disturbances emphasize the all-encompassing impact of night-shift work, and can contribute to the increased risk of various medical conditions. Here, we review the latest scientific evidence regarding the effects of atypical work schedules on the circadian system, sleep and alertness of shift-working populations, and discuss their potential clinical impacts.

Long-Lasting Desynchronization Effects of Coordinated Reset Stimulation Improved by Random Jitters.

Abnormally strong synchronized activity is related to several neurological disorders, including essential tremor, epilepsy, and Parkinson's disease. Chronic high-frequency deep brain stimulation (HF DBS) is an established treatment for advanced Parkinson's disease. To reduce the delivered integral electrical current, novel theory-based stimulation techniques such as coordinated reset (CR) stimulation directly counteract the abnormal synchronous firing by delivering phase-shifted stimuli through multiple stimulation sites. In computational studies in neuronal networks with spike-timing-dependent plasticity (STDP), it was shown that CR stimulation down-regulates synaptic weights and drives the network into an attractor of a stable desynchronized state. This led to desynchronization effects that outlasted the stimulation. Corresponding long-lasting therapeutic effects were observed in preclinical and clinical studies. Computational studies suggest that long-lasting effects of CR stimulation depend on the adjustment of the stimulation frequency to the dominant synchronous rhythm. This may limit clinical applicability as different pathological rhythms may coexist. To increase the robustness of the long-lasting effects, we study randomized versions of CR stimulation in networks of leaky integrate-and-fire neurons with STDP. Randomization is obtained by adding random jitters to the stimulation times and by shuffling the sequence of stimulation site activations. We study the corresponding long-lasting effects using analytical calculations and computer simulations. We show that random jitters increase the robustness of long-lasting effects with respect to changes of the number of stimulation sites and the stimulation frequency. In contrast, shuffling does not increase parameter robustness of long-lasting effects. Studying the relation between acute, acute after-, and long-lasting effects of stimulation, we find that both acute after- and long-lasting effects are strongly determined by the stimulation-induced synaptic reshaping, whereas acute effects solely depend on the statistics of administered stimuli. We find that the stimulation duration is another important parameter, as effective stimulation only entails long-lasting effects after a sufficient stimulation duration. Our results show that long-lasting therapeutic effects of CR stimulation with random jitters are more robust than those of regular CR stimulation. This might reduce the parameter adjustment time in future clinical trials and make CR with random jitters more suitable for treating brain disorders with abnormal synchronization in multiple frequency bands.

Experimental investigation of lean-premixed hydrogen combustion instabilities in a can-annular combustion system

Thermoacoustic interactions in a circumferential network of lean-premixed combustors have a substantial impact on engine-level dynamics in a can-annular gas turbine combustion system. Previous experimental and numerical studies have focused on identifying the formation of large-scale interaction patterns and the modal dynamics of multiple eigenmodes. Since those investigations were primarily concerned with low-frequency interactions between adjacent combustors, there are currently no experimental observations that enable decisive discrimination between low- and high-frequency can-annular combustion instabilities. Here, we use pure hydrogen-air flame ensembles to trigger higher acoustic modes in four-coupled lean-premixed combustors, ultimately to understand the potential influence of self-excited instabilities on the spatiotemporal evolution of a can-annular system. The use of lean-premixed hydrogen-air flames enables measurements of previously unidentified phenomena, particularly in association with the excitation of high acoustic modes up to approximately 1.3 kHz. We demonstrate that self-excited standing azimuthal modes can be excited in the annular cross-talk section, particularly when the phase dynamics of the upstream flame tube sections are defined by alternating anti-phase oscillations. In this case, the temporal evolution of the can-annular system is governed by twofold degeneracy, incorporating an alternating push-pull mode in the longitudinal direction and a standing azimuthal mode in the circumferential direction at the same frequency. Based on experimental observations and Helmholtz simulations, we also show that a mixed state of synchronization and desynchronization can arise simultaneously as a result of symmetry breaking. The coexistence of coherent and incoherent motions is observed to be controlled by interactions between two closely spaced, but slightly misaligned, localized in-phase modes; this observation demonstrates experimentally the existence of a chiral state in can-annular thermoacoustics. The present results, for the first time, reveal a variety of phenomena involved in the response of a can-annular combustion system to higher frequency acoustic perturbations.

Desynchronization of jammed oscillators by avalanches

Synchrony is inevitable in many oscillating systems -- from the canonical alignment of two ticking grandfather clocks, to the mutual entrainment of beating flagella or spiking neurons. Yet both biological and manmade systems provide striking examples of spontaneous desynchronization, such as failure cascades in alternating current power grids or neuronal avalanches in the mammalian brain. Here, we generalize classical models of synchronization among heterogenous oscillators to include short-range phase repulsion among individuals, a property that abets the emergence of a stable desynchronized state. Surprisingly, we find that our model exhibits self-organized avalanches at intermediate values of the repulsion strength, and that these avalanches have similar statistical properties to cascades seen in real-world systems such as neuronal avalanches. We find that these avalanches arise due to a critical mechanism based on competition between mean field recruitment and local displacement, a property that we replicate in a classical cellular automaton model of traffic jams. We exactly solve our system in the many-oscillator limit, and obtain analytical results relating the onset of avalanches or partial synchrony to the relative heterogeneity of the oscillators, and their degree of mutual repulsion. Our results provide a minimal analytically-tractable example of complex dynamics in a driven critical system.

The impact of chaotic saddles on the synchronization of complex networks of discrete-time units

A chaotic saddle is a common nonattracting chaotic set well known for generating finite-time chaotic behavior in low and high-dimensional systems. In general, dynamical systems possessing chaotic saddles in their state-space exhibit irregular behavior with duration lengths following an exponential distribution. However, when these systems are coupled into networks the chaotic saddle plays a role in the long-term dynamics by trapping network trajectories for times that are indefinitely long. This process transforms the network’s high-dimensional state-space by creating an alternative persistent desynchronized state coexisting with the completely synchronized one. Such coexistence threatens the synchronized state with vulnerability to external perturbations. We demonstrate the onset of this phenomenon in complex networks of discrete-time units in which the synchronization manifold is perturbed either in the initial instant of time or in arbitrary states of its asymptotic dynamics. The role of topological asymmetries of Erdös–Rényi and Barabási–Albert graphs are investigated. Besides, the required coupling strength for the occurrence of trapping in the chaotic saddle is unveiled.

Emergence of order from chaos: A phenomenological model of coupled oscillators

Abstract This paper aims to study the transition to order from chaos using a mathematical model of coupled non-identical oscillators. In the course of our analysis, we adopt a different control parameter other than the conventional parameters: coupling strength and frequency-mismatch, generally used in literature to obtain the aforementioned transition. Both the interacting oscillators become periodic, and they lead to the synchronized state as the control parameter changes monotonically. Initially, the participating oscillators, with low amplitude of oscillations, are in the chaotic desynchronized state. Besides, during the periodic oscillations, the oscillators exhibit high amplitude of oscillations. We illustrate the corresponding results using two examples of coupled oscillators. Such emergence of order from chaos with an accompanying increase in amplitude is ascertained in various numerical simulations and experimental observations.

Local cortical desynchronization and pupil-linked arousal differentially shape brain states for optimal sensory performance.

Instantaneous brain states have consequences for our sensation, perception, and behaviour. Fluctuations in arousal and neural desynchronization likely pose perceptually relevant states. However, their relationship and their relative impact on perception is unclear. We here show that, at the single-trial level in humans, local desynchronization in sensory cortex (expressed as time-series entropy) versus pupil-linked arousal differentially impact perceptual processing. While we recorded electroencephalography (EEG) and pupillometry data, stimuli of a demanding auditory discrimination task were presented into states of high or low desynchronization of auditory cortex via a real-time closed-loop setup. Desynchronization and arousal distinctly influenced stimulus-evoked activity and shaped behaviour displaying an inverted u-shaped relationship: States of intermediate desynchronization elicited minimal response bias and fastest responses, while states of intermediate arousal gave rise to highest response sensitivity. Our results speak to a model in which independent states of local desynchronization and global arousal jointly optimise sensory processing and performance.

Occasional uncoupling overcomes measure desynchronization.

Owing to the absence of the phase space attractors in the Hamiltonian dynamical systems, the concept of the identical synchronization between the dissipative systems is inapplicable to the Hamiltonian systems for which, thus, one defines a related generalized phenomenon known as the measure synchronization. A coupled pair of Hamiltonian systems-the full coupled system also being Hamiltonian-can possibly be in two types of measure synchronized states: quasiperiodic and chaotic. In this paper, we take representative systems belonging to each such class of the coupled systems and highlight that, as the coupling strengths are varied, there may exist intervals in the ranges of the coupling parameters at which the systems are measure desynchronized. Subsequently, we illustrate that as a coupled system evolves in time, occasionally switching off the coupling when the system is in the measure desynchronized state can bring the system back in measure synchrony. Furthermore, for the case of the occasional uncoupling being employed periodically and the corresponding time-period being small, we analytically find the values of the on-fraction of the time-period during which measure synchronization is effected on the corresponding desynchronized state.

Huygens’ synchronization experiment revisited: luck or skill?

In a letter to the Royal Society of London in February of 1665, Christiaan Huygens described ‘an odd kind of sympathy’ between two pendulums mounted side by side on a wooden beam, which inspired the modern studies of synchronization of coupled nonlinear oscillators. Despite the growth of synchronization studies in a variety of disciplines, the original phenomenon described by Huygens remains a puzzle to researchers. Here, by placing two mechanical metronomes on top of a freely moving plastic board, we revisit the synchronization experiment conducted by Huygens. Experimental results show that by introducing a small mismatch to the natural frequencies of the metronomes, the probability of generating the anti-phase synchronization (APS) state, i.e. the ‘odd sympathy’ described by Huygens, can clearly be increased. By numerical simulations of the system dynamics, we conduct a detailed analysis of the influence of frequency mismatch on APS. It is found that as the frequency mismatch increases from zero, the attracting basin of the APS is gradually enlarged and, in the meantime, the basin of the in-phase synchronization (IPS) is reduced. However, as the frequency mismatch exceeds some critical value, both the basins of APS and IPS suddenly disappear, resulting in the desynchronization states. The impacts of the friction coefficient and synchronization precision on APS are also studied, and it is found that with the increase of the friction coefficient and the precision requirement of APS, the critical frequency mismatch for desynchronization will decrease. Our study indicates that, instead of luck, Huygens might have introduced, deliberately and elaborately, a small frequency mismatch to the pendulums in his experiment for generating the odd sympathy.

Cortical travelling waves: mechanisms and computational principles.

Multichannel recording technologies have revealed travelling waves of neural activity in multiple sensory, motor and cognitive systems. These waves can be spontaneously generated by recurrent circuits or evoked by external stimuli. They travel along brain networks at multiple scales, transiently modulating spiking and excitability as they pass. Here, we review recent experimental findings that have found evidence for travelling waves at single-area (mesoscopic) and whole-brain (macroscopic) scales. We place these findings in the context of the current theoretical understanding of wave generation and propagation in recurrent networks. During the large low-frequency rhythms of sleep or the relatively desynchronized state of the awake cortex, travelling waves may serve a variety of functions, from long-term memory consolidation to processing of dynamic visual stimuli. We explore new avenues for experimental and computational understanding of the role of spatiotemporal activity patterns in the cortex.

ADHD and Temporality: A Desynchronized Way of Being in the World

ABSTRACTADHD is, I argue, an impairment in sense of time and a matter of difference in rhythm; it can be understood as a certain being in the world, or more specifically, as a disruption in the experience of time and a state of desynchronization and arrhythmia. Through excerpts of interviews with adults diagnosed with ADHD and observations, I illustrate how impairment in time is manifested in an embodied experience of being out of sync. I suggest that the experience of ADHD is characterized as 1) an inner restlessness and bodily arrhythmia; 2) an intersubjective desynchronization between the individual and its surroundings; and 3) a feeling of lagging behind socially due to difficulties in social skills. In closing, I argue that an increasingly accelerating society is augmenting the experience of being out of sync rather than eliminating it.

State-dependent and cell type-specific temporal processing in auditory thalamocortical circuit.

Ongoing spontaneous activity in cortical circuits defines cortical states, but it still remains unclear how cortical states shape sensory processing across cortical laminae and what type of response properties emerge in the cortex. Recording neural activity from the auditory cortex (AC) and medial geniculate body (MGB) simultaneously with electrical stimulations of the basal forebrain (BF) in urethane-anesthetized rats, we investigated state-dependent spontaneous and auditory-evoked activities in the auditory thalamocortical circuit. BF stimulation induced a short-lasting desynchronized state, with sparser firing and increased power at gamma frequency in superficial layers. In this desynchronized state, the reduction in onset response variability in both AC and MGB was accompanied by cell type-specific firing, with decreased responses of cortical broad spiking cells, but increased responses of cortical narrow spiking cells. This onset response was followed by distinct temporal evolution in AC, with quicker rebound firing in infragranular layers. This temporal profile was associated with improved processing of temporally structured stimuli across AC layers to varying degrees, but not in MGB. Thus, the reduction in response variability during the desynchronized state can be seen subcortically whereas the improvement of temporal tuning emerges across AC layers, emphasizing the importance of state-dependent intracortical processing in hearing.

Timing of neuropeptide coupling determines synchrony and entrainment in the mammalian circadian clock.

Robust synchronization is a critical feature of several systems including the mammalian circadian clock. The master circadian clock in mammals consists of about 20000 ‘sloppy’ neuronal oscillators within the hypothalamus that keep robust time by synchronization driven by inter-neuronal coupling. The complete understanding of this synchronization in the mammalian circadian clock and the mechanisms underlying it remain an open question. Experiments and computational studies have shown that coupling individual oscillators can achieve robust synchrony, despite heterogeneity and different network topologies. But, much less is known regarding the mechanisms and circuits involved in achieving this coupling, due to both system complexity and experimental limitations. Here, we computationally study the coupling mediated by the primary coupling neuropeptide, vasoactive intestinal peptide (VIP) and its canonical receptor, VPAC2R, using the transcriptional elements and generic mode of VIP-VPAC2R signaling. We find that synchrony is only possible if VIP (an inducer of Per expression) is released in-phase with activators of Per expression. Moreover, anti-phasic VIP release suppresses coherent rhythms by moving the network into a desynchronous state. Importantly, experimentally observed rhythms in VPAC2R have little effect on network synchronization, but can improve the amplitude of the SCN network rhythms while narrowing the network entrainment range. We further show that these findings are valid across several computational network models. Thus, we identified a general design principle to achieve robust synchronization: An activating coupling agent, such as VIP, must act in-phase with the activity of core-clock promoters. More generally, the phase of coupling is as critical as the strength of coupling from the viewpoint of synchrony and entrainment.

DESYNCHRONIZATION OF TWO COUPLED LIMIT-CYCLE OSCILLATORS USING AN ASTROCYTE-INSPIRED CONTROLLER

Astrocytes have potential to break synchrony between neurons. Authors' recent researches reveal that astrocytes vary the synchronization threshold and provide an appropriate feedback control in stabilizing neural activities. In this study, we propose an astrocyte-inspired controller for desynchronization of two coupled limit-cycle oscillators as a minimal network model. The design procedure consists of two parts. First, based on the astrocyte model, the structure of the dynamic controller is suggested. Then, to have an efficient controller, parameters of controller are tuned through an optimization algorithm. The proposed bio-inspired controller takes advantages of three important properties: (1) the controller desynchronizes the oscillators without any undesirable effects (e.g. stopping, annihilating or starting divergent oscillations); (2) it consumes little effort to preserve the desirable desynchronized state; and (3) the controller is robust with respect to parameters' variations. Simulation results reveal the ability of the proposed controller.

A proof of the Kuramoto conjecture for a bifurcation structure of the infinite-dimensional Kuramoto model

AbstractThe Kuramoto model is a system of ordinary differential equations for describing synchronization phenomena defined as coupled phase oscillators. In this paper, a bifurcation structure of the infinite-dimensional Kuramoto model is investigated. A purpose here is to prove the bifurcation diagram of the model conjectured by Kuramoto in 1984; if the coupling strength $K$ between oscillators, which is a parameter of the system, is smaller than some threshold ${K}_{c} $, the de-synchronous state (trivial steady state) is asymptotically stable, while if $K$ exceeds ${K}_{c} $, a non-trivial stable solution, which corresponds to the synchronization, bifurcates from the de-synchronous state. One of the difficulties in proving the conjecture is that a certain non-selfadjoint linear operator, which defines a linear part of the Kuramoto model, has the continuous spectrum on the imaginary axis. Hence, the standard spectral theory is not applicable to prove a bifurcation as well as the asymptotic stability of the steady state. In this paper, the spectral theory on a space of generalized functions is developed with the aid of a rigged Hilbert space to avoid the continuous spectrum on the imaginary axis. Although the linear operator has an unbounded continuous spectrum on a Hilbert space, it is shown that it admits a spectral decomposition consisting of a countable number of eigenfunctions on a space of generalized functions. The semigroup generated by the linear operator will be estimated with the aid of the spectral theory on a rigged Hilbert space to prove the linear stability of the steady state of the system. The center manifold theory is also developed on a space of generalized functions. It is proved that there exists a finite-dimensional center manifold on a space of generalized functions, while a center manifold on a Hilbert space is of infinite dimension because of the continuous spectrum on the imaginary axis. These results are applied to the stability and bifurcation theory of the Kuramoto model to obtain a bifurcation diagram conjectured by Kuramoto.