Strange Dynamics in a Fractional Derivative of Complex-Order Network of Chaotic Oscillators

We study the peculiar dynamical features of a fractional derivative of complex-order network. The network is composed of two unidirectional rings of cells, coupled through a "buffer" cell. The network has a Z3 × Z5 cyclic symmetry group. The complex derivative Dα±jβ, with α, β ∈ R+ is a generalization of the concept of integer order derivative, where α = 1, β = 0. Each cell is modeled by the Chen oscillator. Numerical simulations of the coupled cell system associated with the network expose patterns such as equilibria, periodic orbits, relaxation oscillations, quasiperiodic motion, and chaos, in one or in two rings of cells. In addition, fixing β = 0.8, we perceive differences in the qualitative behavior of the system, as the parameter c ∈ [13, 24] of the Chen oscillator and/or the real part of the fractional derivative, α ∈ {0.5, 0.6, 0.7, 0.8, 0.9, 1.0}, are varied. Some patterns produced by the coupled system are constrained by the network architecture, but other features are only understood in the light of the internal dynamics of each cell, in this case, the Chen oscillator. What is more important, architecture and/or internal dynamics?

Synchronization properties of multi-oscillator circadian systems

Dissertation presented to obtain the Ph.D degree in Computational Biology

Bimodal information increases spontaneous interpersonal synchronization of goal directed upper limb movements

When interacting with each other, people often synchronize spontaneously their movements, e.g. during pendulum swinging, chair rocking[5], walking [4][7], and when executing periodic forearm movements[3].Although the spatiotemporal information that establishes the coupling, leading to synchronization, might be provided by several perceptual systems, the systematic study of different sensory modalities contribution is widely neglected. Considering a) differences in the sensory dominance on the spatial and temporal dimension[5] , b) different cue combination and integration strategies [1][2], and c) that sensory information might provide different aspects of the same event, synchronization should be moderated by the type of sensory modality. Here, 9 naïve participants placed a bottle periodically between two target zones, 40 times, in 12 conditions while sitting in front of a confederate executing the same task. The participant could a) see and hear, b) see , c) hear the confederate, d) or audiovisual information about the movements of the confederate was absent. The couple started in 3 different relative positions (i.e., in-phase, anti-phase, out of phase). A retro-reflective marker was attached to the top of the bottles. Bottle displacement was captured by a motion capture system. We analyzed the variability of the continuous relative phase reflecting the degree of synchronization. Results indicate the emergence of spontaneous synchronization, an increase with bimodal information, and an influence of the initial phase relation on the particular synchronization pattern. Results have theoretical implication for studying cue combination in interpersonal coordination and are consistent with coupled oscillator models.

Sensorimotor synchronization when walking side by side with a point light walker

[Excerpt] Synchronization of periodic movements like side-by-side walking [7] is frequently modeled by coupled oscillators [5] and the coupling strength is defined quantitatively [3]. In contrast, in most studies on sensorimotor synchronization (SMS), simple movements like finger taps are synchronized with simple stimuli like metronomes [4]. While the latter paradigm simplifies matters and allows for the assessment of the relative weights of sensory modalities through systematic variation of the stimuli [1], it might lack ecological validity. Conversely, using more complex movements and stimuli might complicate the specification of mechanisms underlying coupling. We merged the positive aspects of both approaches to study the contribution of auditory and visual information on synchronization during side-by-side walking. As stimuli, we used Point Light Walkers (PLWs) and auralized steps sound; both were constructed from previously captured walking individuals [2][6]. PLWs were retro-projected on a screen and matched according to gender, hip height, and velocity. The participant walked for 7.20m side by side with 1) a PLW, 2) steps sound, or 3) both displayed in temporal congruence. Instruction to participants was to synchronize with the available stimuli. [...]

Breakdown and restoration of brain synchronization in blindness

Magdeburg, Univ., Fak. für Naturwiss., Diss., 2015

Chaotic dynamics in credit constrained emerging economies

This paper analyzes the role of financial development as a source of endogenous instability in small open economies. By assuming that firms face credit constraints, our model displays a complex dynamic behavior for intermediate values of the parameter representing the level of financial development of the economy. The basic implication of our model is that economies experiencing a process of financial development are more unstable than both very underdeveloped and very developed economies. Our instability concept means that small shocks have a persistent effect on the long run behavior of the model and also that economies can exhibit cycles with a very high period or even chaotic dynamic patterns.

Wireless GPS-based phase-locked synchronization system for outdoor environment.

Synchronization of data coming from different sources is of high importance in biomechanics to ensure reliable analyses. This synchronization can either be performed through hardware to obtain perfect matching of data, or post-processed digitally. Hardware synchronization can be achieved using trigger cables connecting different devices in many situations; however, this is often impractical, and sometimes impossible in outdoors situations. The aim of this paper is to describe a wireless system for outdoor use, allowing synchronization of different types of - potentially embedded and moving - devices. In this system, each synchronization device is composed of: (i) a GPS receiver (used as time reference), (ii) a radio transmitter, and (iii) a microcontroller. These components are used to provide synchronized trigger signals at the desired frequency to the measurement device connected. The synchronization devices communicate wirelessly, are very lightweight, battery-operated and thus very easy to set up. They are adaptable to every measurement device equipped with either trigger input or recording channel. The accuracy of the system was validated using an oscilloscope. The mean synchronization error was found to be 0.39 μs and pulses are generated with an accuracy of <2 μs. The system provides synchronization accuracy about two orders of magnitude better than commonly used post-processing methods, and does not suffer from any drift in trigger generation.

Tracking of Stepwise Ablation of Persistent Atrial Fibrillation using Synchronization of nearby Electrogams

Intracardiac organization indices such as atrial fibril- lation (AF) cycle length (AFCL) have been used to track the efficiency of stepwise catheter ablation (step-CA) of long-standing persistent AF (pers-AF), however, with lim- ited success. The timing between nearby bipolar intracar- diac electrograms (EGMs) reflects the spatial dynamics of wavelets during AF. The extent of synchronization between EGMs is an indirect measure of AF spatial organization. The synchronization between nearby EGMs during step- CA of pers-AF was evaluated using new indices based on the cross-correlation. The first one (spar(W)) quantifies the sparseness of the cross-correlation of local activation times. The second one (OI(W)) reflects the local concen- tration around the largest peak of the cross-correlation. By computing their relative evolution during step-CA until AF termination (AF-term), we found that OI(W) appeared su- perior to AFCL and spar(W) to track the effect of step-CA "en route" to AF-term.

Binding under Conflict Conditions: State-Space Analysis of Multivariate EEG Synchronization.

Real-world objects are often endowed with features that violate Gestalt principles. In our experiment, we examined the neural correlates of binding under conflict conditions in terms of the binding-by-synchronization hypothesis. We presented an ambiguous stimulus ("diamond illusion") to 12 observers. The display consisted of four oblique gratings drifting within circular apertures. Its interpretation fluctuates between bound ("diamond") and unbound (component gratings) percepts. To model a situation in which Gestalt-driven analysis contradicts the perceptually explicit bound interpretation, we modified the original diamond (OD) stimulus by speeding up one grating. Using OD and modified diamond (MD) stimuli, we managed to dissociate the neural correlates of Gestalt-related (OD vs. MD) and perception-related (bound vs. unbound) factors. Their interaction was expected to reveal the neural networks synchronized specifically in the conflict situation. The synchronization topography of EEG was analyzed with the multivariate S-estimator technique. We found that good Gestalt (OD vs. MD) was associated with a higher posterior synchronization in the beta-gamma band. The effect of perception manifested itself as reciprocal modulations over the posterior and anterior regions (theta/beta-gamma bands). Specifically, higher posterior and lower anterior synchronization supported the bound percept, and the opposite was true for the unbound percept. The interaction showed that binding under challenging perceptual conditions is sustained by enhanced parietal synchronization. We argue that this distributed pattern of synchronization relates to the processes of multistage integration ranging from early grouping operations in the visual areas to maintaining representations in the frontal networks of sensory memory.

Imaging EEG synchronization in schizophrenia patients with S-estimator

Recently a new measure of the cooperative behavior of simultaneous time series was introduced (Carmeli et al. NeuroImage 2005). This measure called S-estimator is defined from the embedding dimension in a state space. S-estimator quantifies the amount of synchronization within a data set by comparing the actual dimensionality of the set with the expected full dimensionality of the asynchronous set. It has the advantage of being a multivariate measure over traditionally used in systems neuroscience bivariate measures of synchronization. Multivariate measures of synchronization are of particular interest for applications in the field of modern multichannel EEG research, since they easily allow mapping of local and/or regional synchronization and are compatible with other imaging techniques. We applied Sestimator to the analysis of EEG synchronization in schizophrenia patients vs. matched controls. The whole-head mapping with S-estimator revealed a specific pattern of local synchronization in schizophrenia patients. The differences in the landscape of synchronization included decreased local synchronization in the territories over occipital and midline areas and increased synchronization over temporal areas. In frontal areas, the S-estimator revealed a tendency for an asymmetry: decreased S-values over the left hemisphere were adjacent to increased values over the right hemisphere. Separate calculations showed reproducibility of this pattern across the main EEG frequency bands. The maintenance of the same synchronization landscape across EEG frequencies probably implies the structural changes in the cortical circuitry of schizophrenia patients. These changes are regionally specific and suggest that schizophrenia is a misconnectivity rather than hypo- or hyper-connectivity disorder.

Synchronization of EEG: bivariate and multivariate measures.

Synchronization behavior of electroencephalographic (EEG) signals is important for decoding information processing in the human brain. Modern multichannel EEG allows a transition from traditional measurements of synchronization in pairs of EEG signals to whole-brain synchronization maps. The latter can be based on bivariate measures (BM) via averaging over pair-wise values or, alternatively, on multivariate measures (MM), which directly ascribe a single value to the synchronization in a group. In order to compare BM versus MM, we applied nine different estimators to simulated multivariate time series with known parameters and to real EEGs.We found widespread correlations between BM and MM, which were almost frequency-independent for all the measures except coherence. The analysis of the behavior of synchronization measures in simulated settings with variable coupling strength, connection probability, and parameter mismatch showed that some of them, including S-estimator, S-Renyi, omega, and coherence, aremore sensitive to linear interdependences,while others, like mutual information and phase locking value, are more responsive to nonlinear effects. Onemust consider these properties together with the fact thatMM are computationally less expensive and, therefore, more efficient for the large-scale data sets than BM while choosing a synchronization measure for EEG analysis.

Abnormal EEG Synchronization Correlates with Demyelination in Alzheimer's Disease

Introduction : The pathological processes caused by Alzheimer's disease (AD) supposedly disrupt communication between and within the distributed cortical networks due to the dysfunction/loss of synapses and myelination breakdown. Indeed, recently (Knyazeva et al. 2008), we have revealed the whole-head topography of EEG synchronization specific to AD. Here we analyze whether and how these abnormalities of synchronization are related to the demyelination of cortico-cortical fibers. Methods : Fifteen newly diagnosed AD patients (CDR 0.5-1) and 15 controls matched for age, participated in the study. Their multichannel (128) EEGs were recorded during 3-5 min at rest. They were submitted to the multivariate phase synchronization (MPS) analysis for mapping regional synchronization. To obtain individual whole-head maps, the MPS was computed for each sensor considering its 2nd nearest topographical neighbors. Separate calculations were performed for the delta, theta, alpha-1/−2, and beta-1/−2 EEG bands. The same subjects were scanned on a 3 Tesla Philips scanner. The protocol included a high-resolution T1-weighted sequence and a Magnetization Transfer Imaging (MTI) acquisition. For each subject, we defined a 3mm thick layer of white matter exactly below the cortical gray matter. The magnetization transfer ratio (MTR) - an estimator of myelination - was calculated for this layer in 39 Brodmann-defined ROIs per hemisphere. To assess the between-group differences, we used a permutation version of Hotelling's T2 test or two-sample T-test (Pcorrected <0.05). For correlation analysis, Spearman Rank Correlation was calculated. Results : In AD patients, we have found an abnormal landscape of synchronization characterized by a decrease in MPS over the fronto-temporal region of the left hemisphere and an increase over the temporo-parieto-occipital regions bilaterally. Also, we have shown a widespread decrease in regional MTR in the AD patients for all the areas excluding motor, premotor, and primary sensory ones. Assuming that AD-related changes in synchronization are associated with demyelination, we hypothesized a correlation between the regional MTR values and MPS values in the hypo- and hyper-synchronized clusters. We found that MPS in the left fronto-temporal hypo-synchronized cluster directly correlates with myelination in BA42-46 of the left hemisphere: the lower the myelination in individual patients, the lower the EEG synchronization. By contrast, in the posterior hyper-synchronized cluster, MPS inversely correlated with myelination, i.e., the lower the myelination, the higher the synchronization. This posterior hyper-synchronization, more characteristic for early-onset AD, probably, results from the initial effect of the disease on cortical inhibition, reducing cortical capacity for decoupling irrelevant connections. Remarkably, it showed different topography of correlations in early- vs. late-onset patients. In the early-onset patients, hyper-synchronization was mainly related to demyelination in posterior BAs, the effect being significant in all the EEG frequency bands. In the late-onset patients, widely distributed correlations were significant for the EEG delta band, suggesting an interaction between the cerebral manifestations of AD and the age of its onset, i.e., topographically selective impairment of cortical inhibition in early-onset AD vs. its wide-spread weakening in old age. Conclusions : Overall, our results document that the degradation of white matter is a significant factor of AD pathogenesis leading to functional dysconnection, the latter being reflected in EEG synchronization abnormalities.

Glutathione Precursor, N-Acetyl-Cysteine, Modulates EEG Synchronization in Schizophrenia Patients

Background: Glutathione (GSH) dysregulation at the gene, protein and functional levels observed in schizophrenia patients, and schizophrenia-like anomalies in GSH deficit experimental models, suggest that genetic glutathione synthesis impairments represent one major risk factor for the disease (Do et al., 2009). In a randomized, double blind, placebo controlled, add-on clinical trial of 140 patients, the GSH precursor N-Acetyl-Cysteine (NAC, 2g/day, 6 months) significantly improved the negative symptoms and reduced sideeffects due to antipsychotics (Berk et al., 2008). In a subset of patients (n=7), NAC (2g/day, 2 months, cross-over design) also improved auditory evoked potentials, the NMDA-dependent mismatch negativity (Lavoie et al, 2008). Methods: To determine whether increased GSH levels would modulate the topography of functional brain connectivity, we applied a multivariate phase synchronization (MPS) estimator (Knyazeva et al, 2008) to dense-array EEGs recorded during rest with eyes closed at the protocol onset, the point of crossover, and at its end. Results: The whole-head imaging revealed a specific synchronization landscape in NAC compared to placebo condition. In particular, NAC increased MPS over frontal and left temporal regions in a frequency-specific manner. The topography and direction of MPS changes were similar and robust in all 7 patients. Moreover, these changes correlated with the changes in the Liddle's score of disorganization, thus linking EEG synchronization to the improvement of the clinical picture. Conclusions: The data suggest an important pathway towards new therapeutic strategies that target GSH dysregulation in schizophrenia. They also show the utility of MPS mapping as a marker of treatment efficacy.

An LMI approach to H∞ synchronization of second-order neutral master-slave systems

The H∞ synchronization problem of the master and slave structure of a second-order neutral master-slave systems with time-varying delays is presented in this paper. Delay-dependent sufficient conditions for the design of a delayed output-feedback control are given by Lyapunov-Krasovskii method in terms of a linear matrix inequality (LMI). A controller, which guarantees H∞ synchronization of the master and slave structure using some free weighting matrices, is then developed. A numerical example has been given to show the effectiveness of the method

Altered Local Beta and Gamma Synchronization in Prefrontal Cortex of Mice with Redox Dysregulation or Maternal Immune Activation

Background: A developmental dysregulation of glutathione (GSH) synthesis leading to oxidative stress, when combined with environmental risk factors (viral infections) generating reactive oxygen species, can play a critical role in inducing schizophrenia phenotypes. GSH deficit induces morphological, physiological and behavioral anomalies analogous to those reported in schizophrenic patients, including disrupted parvalbumine (PV) inhibitory interneuron's integrity and neuronal synchrony (β/γ-oscillations). Methods: We assessed PV immunoreactivity (PV-IR) and local synchronization in prefrontal cortex of two mouse models: (1) mice with a genetic deficit in GSH (GCLM-/-) and (2) mice with prenatal immune activation at embryonic day17 (PolyI:C). Results: Adults from both mice models display reduced PV-IR in prefrontal cortex. In anterior cingulate (ACC) of GCLM-/-, appearance and maturation of PVI are delayed and worsened with peribubertal stress but not in adult one. This effect is reversed by treatment with the GSH precursor N-acetyl-cysteine. The power of beta and gamma oscillations are decreased in ACC of GCLM-/- while they increased in prelimbic cortex of PolyI:C mice. Conclusions: Despite reduced PV-IR in both models, alteration of the synchronization was different, indicating that the structural/functional disruption of the cortical circuitry was partly different in both models. Novel therapeutic strategies are proposed, based on interference with oxidative stress and inflammatory processes.