Reconstruction of coupling structure in network of neuron-like oscillators based on a phase-locked loop (original) (raw)
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Phase-locked oscillations in a neuronal network model
Neurocomputing, 2002
We analyzed the oscillatory activities in a neuronal network model as the basis of synchrony of the activities in the brain. The model consists of two groups of neurons that are interconnected. One group is composed of an excitatory and an inhibitory neuron which are expressed by Hodgkin-Huxley equations. The network shows di erent phase-locked oscillations depending on the structure and intensity of interconnection between groups or coupling of neurons in the group, or the value of synaptic latency. The oscillations include various periodic solutions in which the two groups oscillate not only in in-phase or anti-phase but also in continuously changing phase di erence with the parameters of coupling and latency.
Journal of Neuroscience, 2009
Networks of model neurons were constructed and their activity was predicted using an iterated map based solely on the phase-resetting curves (PRCs). The predictions were quite accurate provided that the resetting to simultaneous inputs was calculated using the sum of the simultaneously active conductances, obviating the need for weak coupling assumptions. Fully synchronous activity was observed only when the slope of the PRC at a phase of zero, corresponding to spike initiation, was positive. A novel stability criterion was developed and tested for all-to-all networks of identical, identically connected neurons. When the PRC generated using N Ϫ 1 simultaneously active inputs becomes too steep, the fully synchronous mode loses stability in a network of N model neurons. Therefore, the stability of synchrony can be lost by increasing the slope of this PRC either by increasing the network size or the strength of the individual synapses. Existence and stability criteria were also developed and tested for the splay mode in which neurons fire sequentially. Finally, N/M synchronous subclusters of M neurons were predicted using the intersection of parameters that supported both between-cluster splay and within-cluster synchrony. Surprisingly, the splay mode between clusters could enforce synchrony on subclusters that were incapable of synchronizing themselves. These results can be used to gain insights into the activity of networks of biological neurons whose PRCs can be measured.
Reconstructing phase dynamics of oscillator networks
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2011
We generalize our recent approach to reconstruction of phase dynamics of coupled oscillators from data [B. Kralemann et al., Phys. Rev. E, 77, 066205 (2008)] to cover the case of small networks of coupled periodic units. Starting from the multivariate time series, we first reconstruct genuine phases and then obtain the coupling functions in terms of these phases. The partial norms of these coupling functions quantify directed coupling between oscillators. We illustrate the method by different network motifs for three coupled oscillators and for random networks of five and nine units. We also discuss nonlinear effects in coupling.
Neurocomputing, 2010
Under the premise of analysis on the dynamic characteristics of the transmission mechanism among the synapses, this paper has modified the coupling term in the Tass's stochastic evolution model of neuronal oscillator population, introduced the variable higher-order coupling term. Then, we have performed the numerical simulation on the modified model. The simulation result shows that the variable coupling mechanism can induce the transition between different cluster states of the neuronal oscillator population, without the external stimulation. Another result from the numerical simulation is that, in the transient process between two different synchronization states caused by the variable coupling mechanism, it is allowed to have a full desynchronization state for a period. However, after the period of desynchronization state, the neuronal oscillator population can still reenter a new synchronization state under the action of the coupling term with the order different from initial condition.
Reconstruction of Network Phase Dynamics from Data
Many dynamical systems, both natural and man-made, are composed of interacting parts. Isolated dynamical systems such as the spiking of neurons, cardiac cells, and electrical circuits are periodic in nature. Mathematically, such periodic systems can be described by a limit cycle oscillator, which can be parameterized in terms of phases. Nowadays it is possible to collect and process enormous amounts of data from the units of many such interacting limit cycle oscillators. However, we do not have enough models of such systems to identify and parameterize the crucial features that must be incorporated into the model.
Reconstructing effective phase connectivity of oscillator networks from observations
New Journal of Physics, 2014
We present a novel approach for recovery of the directional connectivity of a small oscillator network by means of the phase dynamics reconstruction from multivariate time series data. The main idea is to use a triplet analysis instead of the traditional pairwise one. Our technique reveals an effective phase connectivity which is generally not equivalent to a structural one. We demonstrate that by comparing the coupling functions from all possible triplets of oscillators, we are able to achieve in the reconstruction a good separation between existing and non-existing connections, and thus reliably reproduce the network structure.
Network of phase-locking oscillators and a possible model for neural synchronization
Communications in Nonlinear Science and Numerical Simulation, 2011
In order to model the synchronization of brain signals, a three-node fully-connected network is presented. The nodes are considered to be voltage control oscillator neurons (VCON) allowing to conjecture about how the whole process depends on synaptic gains, free-running frequencies and delays. The VCON, represented by phase-locked loops (PLL), are fully-connected and, as a consequence, an asymptotically stable synchronous state appears. Here, an expression for the synchronous state frequency is derived and the parameter dependence of its stability is discussed. Numerical simulations are performed providing conditions for the use of the derived formulae. Model differential equations are hard to be analytically treated, but some simplifying assumptions combined with simulations provide an alternative formulation for the long-term behavior of the fully-connected VCON network. Regarding this kind of network as models for brain frequency signal processing, with each PLL representing a neuron (VCON), conditions for their synchronization are proposed, considering the different bands of brain activity signals and relating them to synaptic gains, delays and free-running frequencies. For the delta waves, the synchronous state depends strongly on the delays. However, for alpha, beta and theta waves, the free-running individual frequencies determine the synchronous state.
Modeling the network dynamics of pulse-coupled neurons
Chaos (Woodbury, N.Y.), 2017
We derive a mean-field approximation for the macroscopic dynamics of large networks of pulse-coupled theta neurons in order to study the effects of different network degree distributions and degree correlations (assortativity). Using the ansatz of Ott and Antonsen [Chaos 18, 037113 (2008)], we obtain a reduced system of ordinary differential equations describing the mean-field dynamics, with significantly lower dimensionality compared with the complete set of dynamical equations for the system. We find that, for sufficiently large networks and degrees, the dynamical behavior of the reduced system agrees well with that of the full network. This dimensional reduction allows for an efficient characterization of system phase transitions and attractors. For networks with tightly peaked degree distributions, the macroscopic behavior closely resembles that of fully connected networks previously studied by others. In contrast, networks with highly skewed degree distributions exhibit differe...
Identification of Couplings in Adaptive Dynamical Networks of Time-Delayed Feedback Oscillators
Mathematics, 2021
An approach to solve the inverse problem of the reconstruction of the network of time-delay oscillators from their time series is proposed and studied in the case of the nonstationary connectivity matrix. Adaptive couplings have not been considered yet for this particular reconstruction problem. The problem of coupling identification is reduced to linear optimization of a specially constructed target function. This function is introduced taking into account the continuity of the nonlinear functions of oscillators and does not exploit the mean squared difference between the model and observed time series. The proposed approach allows us to minimize the number of estimated parameters and gives asymptotically unbiased estimates for a large class of nonlinear functions. The approach efficiency is demonstrated for the network composed of time-delayed feedback oscillators with a random architecture of constant and adaptive couplings in the absence of a priori knowledge about the connectiv...
Uncovering phase-coupled oscillatory networks in electrophysiological data
Human brain mapping, 2015
Phase consistent neuronal oscillations are ubiquitous in electrophysiological recordings, and they may reflect networks of phase-coupled neuronal populations oscillating at different frequencies. Because neuronal oscillations may reflect rhythmic modulations of neuronal excitability, phase-coupled oscillatory networks could be the functional building block for routing information through the brain. Current techniques are not suited for directly characterizing such networks. To be able to extract phase-coupled oscillatory networks we developed a new method, which characterizes networks by phase coupling between sites. Importantly, this method respects the fact that neuronal oscillations have energy in a range of frequencies. As a consequence, we characterize these networks by between-site phase relations that vary as a function of frequency, such as those that result from between-site temporal delays. Using human electrocorticographic recordings we show that our method can uncover ph...