Anticipatory Synchronization Research Articles

Paradoxical roles of inhibitory autapse and excitatory synapse in formation of counterintuitive anticipated synchronization

Different from the common delayed synchronization (DS) in which response appears after stimulation, anticipated synchronization (AS) in unidirectionally coupled neurons denotes a counterintuitive phenomenon in which response of the receiver neuron appears before stimulation of the sender neuron, showing an interesting function of brain to anticipate the future. The dynamical mechanism for the AS remains unclear due to complex dynamics of inhibitory and excitatory modulations. In this article, the paradoxical roles of excitatory synapse and inhibitory autapse in the formation of AS are acquired. Firstly, in addition to the common roles such that inhibitory modulation delays and excitatory modulation advances spike, paradoxical roles of excitatory stimulation to delay spike via type-II phase response and of inhibitory autapse to advance spike are obtained in suitable parameter regions, extending the dynamics and functions of the excitatory and inhibitory modulations. Secondly, AS is related to the paradoxical roles of the excitatory and inhibitory modulations, presenting deep understandings to the AS. Inhibitory autapse induces spike of the receiver neuron advanced to appear before that of the sender neuron at first, and then excitatory synapse plays a delay role to prevent the spike further advanced, resulting in the AS as the advance and delay effects realize a dynamic balance. Lastly, inhibitory autapse with strong advance, middle advance, and weak advance and delay effects induce phase drift (spike of the receiver neuron advances continuously), AS, and DS, respectively, presenting comprehensive relationships between AS and other behaviors. The results present potential measures to modulate AS related to brain function.

Are We in Time? How Predictive Coding and Dynamical Systems Explain Musical Synchrony

Humans tend to anticipate events when they synchronize their actions with sound (such as when they clap to music), which has puzzled scientists for decades. What accounts for this anticipation? We review two theoretical mechanisms for synchrony: predictive coding and dynamical systems. Both theories are grounded in neural activation patterns, but there are important distinctions. We contrast their assumptions, their computations, and their musical applications to anticipatory synchronization.

Neuronal heterogeneity modulates phase synchronization between unidirectionally coupled populations with excitation-inhibition balance.

Several experiments and models have highlighted the importance of neuronal heterogeneity in brain dynamics and function. However, how such a cell-to-cell diversity can affect cortical computation, synchronization, and neuronal communication is still under debate. Previous studies have focused on the effect of neuronal heterogeneity in one neuronal population. Here we are specifically interested in the effect of neuronal variability on the phase relations between two populations, which can be related to different cortical communication hypotheses. It has been recently shown that two spiking neuron populations unidirectionally connected in a sender-receiver configuration can exhibit anticipated synchronization (AS), which is characterized by a negative phase lag. This phenomenon has been reported in electrophysiological data of nonhuman primates and human EEG during a visual discrimination cognitive task. In experiments, the unidirectional coupling could be accessed by Granger causality and can be accompanied by either positive or negative phase difference between cortical areas. Here we propose a model of two coupled populations in which the neuronal heterogeneity can determine the dynamical relation between the sender and the receiver and can reproduce phase relations reported in experiments. Depending on the distribution of parameters characterizing the neuronal firing patterns, the system can exhibit both AS and the usual delayed synchronization regime (DS, with positive phase) as well as a zero-lag synchronization regime and phase bistability between AS and DS. Furthermore, we show that our network can present diversity in their phase relations maintaining the excitation-inhibition balance.

Phase bistability between anticipated and delayed synchronization in neuronal populations.

Two dynamical systems unidirectionally coupled in a sender-receiver configuration can synchronize with a nonzero phase lag. In particular, the system can exhibit anticipated synchronization (AS), which is characterized by a negative phase lag, if the receiver also receives a delayed negative self-feedback. Recently, AS was shown to occur between cortical-like neuronal populations in which the self-feedback is mediated by inhibitory synapses. In this biologically plausible scenario, a transition from the usual delayed synchronization (with positive phase lag) to AS can be mediated by the inhibitory conductances in the receiver population. Here we show that depending on the relation between excitatory and inhibitory synaptic conductances the system can also exhibit phase bistability between anticipated and delayed synchronization. Furthermore, we show that the amount of noise at the receiver and the synaptic conductances can mediate the transition from stable phase locking to a bistable regime and eventually to a phase drift. We suggest that our spiking neuronal populations model could be potentially useful to study phase bistability in cortical regions related to bistable perception.

Anticipated synchronization in human EEG data: Unidirectional causality with negative phase lag.

Understanding the functional connectivity of the brain has become a major goal of neuroscience. In many situations the relative phase difference, together with coherence patterns, has been employed to infer the direction of the information flow. However, it has been recently shown in local field potential data from monkeys the existence of a synchronized regime in which unidirectionally coupled areas can present both positive and negative phase differences. During the counterintuitive regime, called anticipated synchronization (AS), the phase difference does not reflect the causality. Here we investigate coherence and causality at the alpha frequency band (f∼10Hz) between pairs of electroencephalogram (EEG) electrodes in humans during a GO/NO-GO task. We show that human EEG signals can exhibit anticipated synchronization, which is characterized by a unidirectional influence from an electrode A to an electrode B, but the electrode B leads the electrode A in time. To the best of our knowledge, this is the first verification of AS in EEG signals and in the human brain. The usual delayed synchronization (DS) regime is also present between many pairs. DS is characterized by a unidirectional influence from an electrode A to an electrode B and a positive phase difference between A and B which indicates that the electrode A leads the electrode B in time. Moreover we show that EEG signals exhibit diversity in the phase relations: the pairs of electrodes can present in-phase, antiphase, or out-of-phase synchronization with a similar distribution of positive and negative phase differences.

Oscillating synchronization in delayed oscillators with time-varying time delay coupling: Experimental observation.

The time-varying time-delayed (TVTD) systems attract the attention of research communities due to their rich complex dynamics and wide application potentiality. Particularly, coupled TVTD systems show several intriguing behaviors that cannot be observed in systems with a constant delay or no delay. In this context, a new synchronization scenario, namely, oscillating synchronization, was reported by Senthilkumar and Lakshmanan [Chaos 17, 013112 (2007)], which is exclusive to the time-varying time delay systems only. However, like most of the dynamical behavior of TVTD systems, its existence has not been established in an experiment. In this paper, we report the first experimental observation of oscillating synchronization in coupled nonlinear time-delayed oscillators induced by a time-varying time delay in the coupling path. We implement a simple yet effective electronic circuit to realize the time-varying time delay in an experiment. We show that depending upon the instantaneous variation of the time delay, the system shows a synchronization scenario oscillating among lag, complete, and anticipatory synchronization. This study may open up the feasibility of applying oscillating synchronization in engineering systems.

Feedback delays can enhance anticipatory synchronization in human-machine interaction

Research investigating the dynamics of coupled physical systems has demonstrated that small feedback delays can allow a dynamic response system to anticipate chaotic behavior. This counterintuitive phenomenon, termed anticipatory synchronization, has been observed in coupled electrical circuits, laser semi-conductors, and artificial neurons. Recent research indicates that the same process might also support the ability of humans to anticipate the occurrence of chaotic behavior in other individuals. Motivated by this latter work, the current study examined whether the process of feedback delay induced anticipatory synchronization could be employed to develop an interactive artificial agent capable of anticipating chaotic human movement. Results revealed that incorporating such delays within the movement-control dynamics of an artificial agent not only enhances an artificial agent’s ability to anticipate chaotic human behavior, but to synchronize with such behavior in a manner similar to natural human-human anticipatory synchronization. The implication of these findings for the development of human-machine interaction systems is discussed.

Exploring the Phase-Locking Mechanisms Yielding Delayed and Anticipated Synchronization in Neuronal Circuits.

Synchronization is one of the brain mechanisms allowing the coordination of neuronal activity required in many cognitive tasks. Anticipated Synchronization (AS) is a specific type of out-of-phase synchronization that occurs when two systems are unidirectionally coupled and, consequently, the information is transmitted from the sender to the receiver, but the receiver leads the sender in time. It has been shown that the primate cortex could operate in a regime of AS as part of normal neurocognitive function. However it is still unclear what is the mechanism that gives rise to anticipated synchronization in neuronal motifs. Here, we investigate the synchronization properties of cortical motifs on multiple scales and show that the internal dynamics of the receiver, which is related to its free running frequency in the uncoupled situation, is the main ingredient for AS to occur. For biologically plausible parameters, including excitation/inhibition balance, we found that the phase difference between the sender and the receiver decreases when the free running frequency of the receiver increases. As a consequence, the system switches from the usual delayed synchronization (DS) regime to an AS regime. We show that at three different scales, neuronal microcircuits, spiking neuronal populations and neural mass models, both the inhibitory loop and the external current acting on the receiver mediate the DS-AS transition for the sender-receiver configuration by changing the free running frequency of the receiver. Therefore, we propose that a faster internal dynamics of the receiver system is the main mechanism underlying anticipated synchronization in brain circuits.

Inhibitory autapse mediates anticipated synchronization between coupled neurons.

Two identical autonomous dynamical systems unidirectionally coupled in a sender-receiver configuration can exhibit anticipated synchronization (AS) if the receiver neuron also receives a delayed negative self-feedback. Recently, AS was shown to occur in a three-neuron motif with standard chemical synapses where the delayed inhibition was provided by an interneuron. Here, we show that a two-neuron model in the presence of an inhibitory autapse, which is a massive self-innervation present in the cortical architecture, may present AS. The GABAergic autapse regulates the internal dynamics of the receiver neuron and acts as the negative delayed self-feedback required by dynamical systems in order to exhibit AS. In this biologically plausible scenario, a smooth transition from the usual delayed synchronization (DS) to AS typically occurs when the inhibitory conductance is increased. The phenomenon is shown to be robust when model parameters are varied within a physiological range. For extremely large values of the inhibitory autapse the system undergoes to a phase-drift regime in which the receiver is faster than the sender. Furthermore, we show that the inhibitory autapse promotes a faster internal dynamics of the free-running Receiver when the two neurons are uncoupled, which could be the mechanism underlying anticipated synchronization and the DS-AS transition.

Identifying topologies and system parameters of uncertain time-varying delayed complex networks

Node dynamics and network topologies play vital roles in determining the network features and network dynamical behaviors. Thus it is of great theoretical significance and practical value to recover the topology structures and system parameters of uncertain complex networks with available information. This paper presents an adaptive anticipatory synchronization-based approach to identify the unknown system parameters and network topological structures of uncertain time-varying delayed complex networks in the presence of noise. Moreover, during the identification process, our proposed scheme guarantees anticipatory synchronization between the uncertain drive and constructed auxiliary response network simultaneously. Particularly, our method can be extended to several special cases. Furthermore, numerical simulations are provided to verify the effectiveness and applicability of our method for reconstructing network topologies and node parameters. We hope our method can provide basic insight into future research on addressing reconstruction issues of uncertain realistic and large-scale complex networks.

Anticipation in the Polarization Chaos Synchronization of Uni-Directionally Coupled Vertical-Cavity Surface-Emitting Lasers With Polarization-Preserved Optical Injection

We investigate numerically the anticipated synchronization in the two uni-directionally coupled vertical-cavity surface-emitting lasers (VCSELs) as master and slave configuration. The master VCSEL is rendered chaotic state by an isotropic optical feedback and master’s chaotic output uni-directionally injected to a slave VCSEL under polarization-preserved optical injection. The synchronization quality and lag time between lasers are obtained by performing cross-correlation analysis. When the laser’s parameters are identical, a regime of anticipatory synchronization is found in both of the linearly polarized mode dynamics of the master and slave lasers, if the feedback delay time is greater than the coupling time. Anticipation is robust to a small variation in injection rate, frequency detuning, and laser’s internal parameter mismatches, but the synchronization is not complete. Injection-locking synchronization regime occurs between master and slave lasers for higher injection, positive detuning, and larger mismatch in the internal parameters. We show the mapping of synchronization quality, sustenance of anticipatory synchronization and switching of regimes in the injection rate and parameter mismatch plane. The anticipation maintained even for higher injection rates if mismatch is introduced in certain internal parameters.

Anticipated synchronization in neuronal circuits unveiled by a phase-response-curve analysis.

Anticipated synchronization (AS) is a counterintuitive behavior that has been observed in several systems. When AS occurs in a sender-receiver configuration, the latter can predict the future dynamics of the former for certain parameter values. In particular, in neuroscience AS was proposed to explain the apparent discrepancy between information flow and time lag in the cortical activity recorded in monkeys. Despite its success, a clear understanding of the mechanisms yielding AS in neuronal circuits is still missing. Here we use the well-known phase-response-curve (PRC) approach to study the prototypical sender-receiver-interneuron neuronal motif. Our aim is to better understand how the transitions between delayed to anticipated synchronization and anticipated synchronization to phase-drift regimes occur. We construct a map based on the PRC method to predict the phase-locking regimes and their stability. We find that a PRC function of two variables, accounting simultaneously for the inputs from sender and interneuron into the receiver, is essential to reproduce the numerical results obtained using a Hodgkin-Huxley model for the neurons. On the contrary, the typical approximation that considers a sum of two independent single-variable PRCs fails for intermediate to high values of the inhibitory coupling strength of the interneuron. In particular, it loses the delayed-synchronization to anticipated-synchronization transition.

Anticipatory synchronization via low-dimensional filters

An anticipatory chaotic synchronization scheme based on a low-order all-pass filter is proposed. The filter is designed as a Padé approximation to the transfer function of an ideal delay line, which is used in a standard Voss scheme. We show that despite its simplicity, the filter works in an anticipatory scheme as well as an ideal delay line. It provides extremely small synchronization error in the whole interval of anticipation time where the anticipatory manifold is stable. The efficacy of our scheme is explained by an analytically solvable model of unidirectionally coupled unstable spirals and confirmed numerically by an example of unidirectionally coupled chaotic Rössler systems.

Inhibitory loop robustly induces anticipated synchronization in neuronal microcircuits

We investigate the synchronization properties between two excitatory coupled neurons in the presence of an inhibitory loop mediated by an interneuron. Dynamic inhibition together with noise independently applied to each neuron provide phase diversity in the dynamics of the neuronal motif. We show that the interplay between the coupling strengths and the external noise controls the phase relations between the neurons in a counterintuitive way. For a master-slave configuration (unidirectional coupling) we find that the slave can anticipate the master, on average, if the slave is subject to the inhibitory feedback. In this nonusual regime, called anticipated synchronization (AS), the phase of the postsynaptic neuron is advanced with respect to that of the presynaptic neuron. We also show that the AS regime survives even in the presence of unbalanced bidirectional excitatory coupling. Moreover, for the symmetric mutually coupled situation, the neuron that is subject to the inhibitory loop leads in phase.

A symbolic information approach to determine anticipated and delayed synchronization in neuronal circuit models.

The phenomenon of synchronization between two or more areas of the brain coupled asymmetrically is a relevant issue for understanding mechanisms and functions within the cerebral cortex. Anticipated synchronization (AS) refers to the situation in which the receiver system synchronizes to the future dynamics of the sender system while the intuitively expected delayed synchronization (DS) represents exactly the opposite case. AS and DS are investigated in the context of causal information formalism. More specifically, we use a multi-scale symbolic information-theory approach for discriminating the time delay displayed between two areas of the brain when they exchange information.

Reconstructing the directionality of coupling between cortical populations with negative phase lag

Understanding how information is processed in the brain is one of the key areas in neuroscience research.Different tools have been employed to reconstruct directional influence and to infer the effective connectivity between distinct brain regions. Particularly, it has been shown [1] that in non-linear delay-coupled oscillating systems exhibiting a negative phase lag, Granger causality (GC) might not provide the correct direction of information flow (from the driver to the receiver). Such systems have been studied before in the theoretical framework of Anticipated Synchronization (AS) developed in the field of dynamical systems [2]. This counterintuitive synchronization regime can be a stable solution of two dynamical systems coupled in a master-slave (driver-receiver) configuration when the slave receives a negative delayed self-feedback. Recently, it has been shown that unidirectional coupled neuronal population models can also exhibit AS [3]. In these cortical like populations the delayed feedback has been replaced by a dynamical inhibitory loop mediated by interneurons. Here we show that in these biologically plausible models, GC provides the correct directionality of the coupling for both positive and negative phase differences. In fact, when compared to experimental data in the primate cortex our model reproduces experimental phase lags, coherence spectra and GC spectra [3].

Self-Organized Near-Zero-Lag Synchronization Induced by Spike-Timing Dependent Plasticity in Cortical Populations.

Several cognitive tasks related to learning and memory exhibit synchronization of macroscopic cortical areas together with synaptic plasticity at neuronal level. Therefore, there is a growing effort among computational neuroscientists to understand the underlying mechanisms relating synchrony and plasticity in the brain. Here we numerically study the interplay between spike-timing dependent plasticity (STDP) and anticipated synchronization (AS). AS emerges when a dominant flux of information from one area to another is accompanied by a negative time lag (or phase). This means that the receiver region pulses before the sender does. In this paper we study the interplay between different synchronization regimes and STDP at the level of three-neuron microcircuits as well as cortical populations. We show that STDP can promote auto-organized zero-lag synchronization in unidirectionally coupled neuronal populations. We also find synchronization regimes with negative phase difference (AS) that are stable against plasticity. Finally, we show that the interplay between negative phase difference and STDP provides limited synaptic weight distribution without the need of imposing artificial boundaries.

Structure Identification of Uncertain Complex Networks Based on Anticipatory Projective Synchronization.

This paper investigates a method to identify uncertain system parameters and unknown topological structure in general complex networks with or without time delay. A complex network, which has uncertain topology and unknown parameters, is designed as a drive network, and a known response complex network with an input controller is designed to identify the drive network. Under the proposed input controller, the drive network and the response network can achieve anticipatory projective synchronization when the system is steady. Lyapunov theorem and Barbǎlat’s lemma guarantee the stability of synchronization manifold between two networks. When the synchronization is achieved, the system parameters and topology in response network can be changed to equal with the parameters and topology in drive network. A numerical example is given to show the effectiveness of the proposed method.

Amplitude death and synchronized states in nonlinear time-delay systems coupled through mean-field diffusion

We explore and experimentally demonstrate the phenomena of amplitude death (AD) and the corresponding transitions through synchronized states that lead to AD in coupled intrinsic time-delayed hyperchaotic oscillators interacting through mean-field diffusion. We identify a novel synchronization transition scenario leading to AD, namely transitions among AD, generalized anticipatory synchronization (GAS), complete synchronization (CS), and generalized lag synchronization (GLS). This transition is mediated by variation of the difference of intrinsic time-delays associated with the individual systems and has no analogue in non-delayed systems or coupled oscillators with coupling time-delay. We further show that, for equal intrinsic time-delays, increasing coupling strength results in a transition from the unsynchronized state to AD state via in-phase (complete) synchronized states. Using Krasovskii-Lyapunov theory, we derive the stability conditions that predict the parametric region of occurrence of GAS, GLS, and CS; also, using a linear stability analysis, we derive the condition of occurrence of AD. We use the error function of proper synchronization manifold and a modified form of the similarity function to provide the quantitative support to GLS and GAS. We demonstrate all the scenarios in an electronic circuit experiment; the experimental time-series, phase-plane plots, and generalized autocorrelation function computed from the experimental time series data are used to confirm the occurrence of all the phenomena in the coupled oscillators.

Anticipated synchronization in neuronal motifs

Anticipated synchronization (AS) is a counterintuitive stable dynamical regime discovered by Voss in the last decade [1]. It consists in the stable synchronized regime between two identical autonomous dynamical systems coupled (unidirectionally) in a master-slave (MS) configuration, if the slave also receives a negative delayed self-feedback. In such regime the slave predicts the master. Although AS has shown to be stable in a variety of theoretical studies [1-3] and in experimental observations [4] with semiconductor lasers and electronic circuits, studies in biological and neuronal systems are still lacking. The first verification of AS in neuronal models was done between two FitzHugh-Nagumo neurons coupled in a MS configuration with negative delayed self-feedback and driven by white noise [2]. In neuronal networks, AS means that the slave (post-synaptic) neuron can fire spikes right before the master (pre-synaptic) neuron. However the slave delayed self-feedback that induces the anticipated synchronization as suggested by Voss is unrealistic in neuronal circuitry. Recently, it has been shown that in a biologically plausible neuronal model, the self-feedback can be replaced by an inhibitory loop mediated by an interneuron and chemical synapses [5]. This master-slave-interneuron motif exhibits the usual delay synchronized (DS) regime for small values of the inhibitory synaptic conductance (g) as well as the AS regime for larger g. Moreover, the time delay between consecutive spikes of the master and the slave neurons is a function of the synaptic conductances. Both regimes were shown to be stable for a large set of parameters, different external currents, structural motif and neuron models [6]. Here we investigate the robustness of AS for others motifs, larger populations, neuronal heterogeneity and noise. In all the situations the transition from DS to AS is continuous and smooth.