International Journal of Bifurcation and Chaos

The general problem of brain mechanisms involved in perception can now be studied directly by means of new analysis–methods for the activity of large population of neurons. These methods range from indirect means of measuring changes in cerebral blood flow in local regions of the human cortex (functional magnetic resonance imaging, fMRI), or changes in the electrical activity of the human brain with EEG-recording with topological distributed macroelectrodes, to the use of chronically implanted multiple microelectrodes in primates. fMRI has the disadvantage of low temporal resolution and with multiple microelectrodes long distance measurements cannot yet be properly performed. Accordingly, recording of macro-activity (EEG/ERP or MEG) with a time resolution of millisecond-range is the most possibly adequate method to measure the dynamic properties of memory and the integrative brain function.

Since neuroscientists have come to the general conclusion that large numbers of different brain regions have to cooperate for any brain function, the analysis of relationships between different regions of the brain is becoming more and more important.

Before new progresses and importance of EEG studies research became clear, scientists working with macrodynamics of the brain had a long way to go, in order to elucidate brain functioning. In this tutorial report we explain in a narrative way the developments leading to the concept of Macrodynamics in search of an integrative brain function. Moreover, elements of a brain theory, which we call neurons-brain theory describing the dynamics of electrical activity in the whole brain, are introduced. The concept of superbinding in integrative brain function, which emerged from experimental data, is a consequence of this theory.

The study of language, its processing and its bearing on human cortical processes are all extensive domains of investigation in their own right. In this overview tutorial we limit ourselves to a sample of core illustrative issues. Our central aim is to demonstrate how complexity within the language faculty arises from two a priori distinct sources: the computational complexity inherent in the grammar of the language system itself and the procedural complexity resulting from marshalling processing resources in order to produce or interpret utterances that correspond to the grammar. Distinguishing between these two sources of complexity is a current goal in investigations of the human language faculty. The combination of quantitative approaches with newer qualitative approaches to the analysis of electro-cortical behavior associated with carefully controlled language paradigms represents a new approach to clarifying this central issue.

We present different tests for phase synchronization which improve the procedures currently used in the literature. This is accomplished by using a two-sample test setup and by utilizing insights and methods from directional statistics and bootstrap theory. The tests differ in the generality of the situation in which they can be applied as well as in their complexity, including computational cost. A modification of the resampling technique of the bootstrap is introduced, making it possible to fully utilize data from time series.

A method for the multivariate analysis of statistical phase synchronization phenomena in empirical data is presented. A first statistical approach is complemented by a stochastic dynamic model, to result in a data analysis algorithm which can in a specific sense be shown to be a generic multivariate statistical phase synchronization analysis. The method is applied to EEG data from a psychological experiment, obtaining results which indicate the relevance of this method in the context of cognitive science as well as in other fields.

There is hardly a more important sensory modality for humans and other mammals than vision. The first and best-known part of the visual system is the retina, which is not a mere photoreceptor or static camera but a sophisticated feature preprocessor with continuous input and several parallel output channels. These interacting channels represent the visual scene. Never before has it been known in neuroscience how these channels build up a "visual language". Our mammalian retina model can generate the elements of this visual language. In the present paper the design steps of the implementation of the multilayer CNN retinal model is shown. It is rare that an analogic CNN algorithm has such a sophisticated series of different complex dynamics, meanwhile it is feasible on a recently fabricated complex cell CNN-UM chip. The mammalian retina model is decomposed into a full-custom mixed-signal chip that embeds digitally programmable analog parallel processing and distributed image memory on a common silicon substrate. The chip was designed and manufactured in a standard 0.5 μm CMOS technology and contains approximately 500,000 transistors. It consists of 1024 processing units arranged into a 32×32 grid. The functional features of the chip are in accordance with the second-order complex cell CNN-UM architecture: two CNN layers with programmable inter- and intra-layer connections between cells as well as programmable layer time constants. The uniqueness of this approach, among others, lies in the reprogrammability, i.e. the openness to any new discovery, even after a possible retinal implementation.

The present report describes the dynamic foundations of long-standing experimental work in the field of oscillatory dynamics in the human and animal brain. It aims to show the role of multiple oscillations in the integrative brain function, memory, and complex perception by a recently introduced conceptional framework: the super-synergy in the whole brain. Results of recent experiments related to the percept of the grandmother-face support our concept of super-synergy in the whole brain in order to explain manifestation of Gestalts and Memory-Stages. This report may also provide new research avenues in macrodynamics of the brain.

During reading, our eyes perform complicated sequences of fixations on words. Stochastic models of eye movement control suggest that this seemingly erratic behavior can be attributed to noise in the oculomotor system and random fluctuations in lexical processing. Here, we present a qualitative analysis of a recently published dynamical model [Engbert et al., 2002] and propose that deterministic nonlinear control accounts for much of the observed complexity of eye movement patterns during reading. Based on a symbolic coding technique we analyze robust statistical features of simulated fixation sequences.

In many signal processing applications, especially in the analysis of complex physiological systems, an important problem is to detect and quantify the interdependencies between signals (or time series). In this paper, we focus on asymmetrical relations between two time series with the aim of quantification of the directional influences between them in the sense of "who drives whom and how strongly". To meet this aim, we modify the mixed state analysis, which was proposed by Wiesenfeldt et al. [2001] to detect primarily the nature of the coupling (unidirectional or bidirectional), for the quantification of the strength of coupling in each direction. We introduce the predictability improvement of one time series by additional consideration of another time series. The newly developed measure is an analogue of the information theoretic concept of transfer entropy and is applicable to short time series. We demonstrate the application of this approach to coupled deterministic systems and to EEG data.

Semantics is the essence of human communication. It concerns the manufacture and use of symbols as representations to exchange meanings. Information technology is faced with the problem of using intelligent machines as intermediaries for interpersonal communication. The problem of designing such semantic machines has been intractable because brains and machines work on very different principles. Machines process information that is fed to them. Brains construct hypotheses and test them by acting and sensing. Brains do not process information because the intake through the senses is infinite. Brains sample information, hold it briefly, construct meaning, and then discard the information. A solution to the problem of communication with machines is to simulate how brains create meaning and express it as information by making a symbol to represent the meaning to another brain in pairwise communication. An understanding of the neurodynamics by which brains create meaning and represent it may enable engineers to build devices with which they can communicate pairwise, as they do now with colleagues.

It is well-known from psycholinguistic literature that the human language processing system exhibits preferences when sentence constituents are ambiguous with respect to their grammatical function. Generally, many theories assume that an interpretation towards the subject is preferred in such cases. Later disambiguations which contradict such a preference induce enhanced processing difficulty (i.e. reanalysis) which reflects itself in late positive deflections (P345/P600) in event-related brain potentials (ERPs). In the case of phoric elements such as pronouns, a second strategy is known according to which an ambiguous pronoun preferentially receives the grammatical function that its antecedent has (parallel function strategy). In an ERP study, we show that this strategy can in principle override the general subject preference strategy (known for both pronominal and nonpronominal constituents) and induce an object preference, in case that the pronoun's antecedent is itself an object. Interestingly, the revision of a subject preference leads to a P600 component, whereas the revision of an object preference induces an earlier positivity (P345). In order to show that the latter component is indeed a positivity and not an N400-like negativity in the same time range, we apply an additional analysis based on symbolic dynamics which allows to determine the polarity of an ERP effect on purely methodological grounds. With respect to the two positivities, we argue that the latency differences reflect qualitative differences in the reanalysis processes.

In this paper we demonstrate the potential of the cellular nonlinear/neural network paradigm (CNN) that of the analogic cellular computer architecture (called CNN Universal Machine — CNN-UM) in modeling different parts and aspects of the nervous system. The structure of the living sensory systems and the CNN share a lot of features in common: local interconnections ("receptive field architecture"), nonlinear and delayed synapses for the processing tasks, the potentiality of feedback and using the advantages of both the analog and logic signal-processing mode. The results of more than ten years of cooperative work of many engineers and neurobiologists have been collected in an atlas: what we present here is a kind of selection from these studies emphasizing the flexibility of the CNN computing: visual, tactile and auditory modalities are concerned.

Short-time correlations in multivariate time series are notoriously difficult to detect. Extending the classical concept of correlation, we present a method to tackle this problem with little computational cost. In essence, the method uncovers multidimensional phase-locking and is especially useful for revealing changes of the dynamical coupling between different brain areas. The approach also permits us to estimate the shortest time-window in which the coupling occurs. Furthermore, the coupling can be quantified by a measure that defines a metric space. Therefore it may be used to identify task-dependent coupling hierarchies between two brain areas. We illustrate the analysis technique by studying the dynamical coupling between two brain regions involved in olfactory processing in the honeybee. We show that the neural activity in both areas is coupled with each other and that the coupling increases significantly during odor processing.

We describe a part of the stimulus sentences of a German language processing ERP experiment using a context-free grammar and represent different processing preferences by its unambiguous partitions. The processing is modeled by deterministic pushdown automata. Using a theorem proven by Moore, we map these automata onto discrete time dynamical systems acting at the unit square, where the processing preferences are represented by a control parameter. The actual states of the automata are rectangles lying in the unit square that can be interpreted as cylinder sets in the context of symbolic dynamics theory. We show that applying a wrong processing preference to a certain input string leads to an unwanted invariant set in the parsers dynamics. Then, syntactic reanalysis and repair can be modeled by a switching of the control parameter — in analogy to phase transitions observed in brain dynamics. We argue that ERP components are indicators of these bifurcations and propose an ERP-like measure of the parsing model.

Recently, neurobiologists have discovered axons on neurons which synapse on the same neuron's dendrites — so-called autapses. It is not yet clear what functional significance autapses offer for neural behavior. This is an ideal case for using a physical simulation to investigate how an autapse alters the firing of a neuron. We simulated a neural basket cell via the Hodgkin–Huxley equations and implemented an autapse which feeds back onto the soma of the neuron. The behavior of the cell was compared with and without autaptic feedback. Our artificial autapse neuron (AAN) displays oscillatory behavior which is not observed for the same model neuron without autapse. The neuron oscillates between two functional states: one where it fires at high frequency and another where firing is suppressed. This behavior is called "spike bursting" and represents a common pattern recorded from cerebral neurons.

Affective disorders tend to be recurrent and progressive and illness patterns typically evolve from isolated episodes at the beginning to more rapid, rhythmic and finally irregular "chaotic" mood patterns. Chararacteristic timecourse and disease patterns have prompted the consideration of nonlinear dynamics and chaos. In this paper we review some of our recent work where we addressed the relevance of nonlinear, stochastic and resulting cooperative dynamics for disease patterns and temporal course of affective disorders by use of a computational approach.

The present work reviews briefly a segmentation method and a modeling approach for multivariate quasi-stationary data. The combination of both parts allows the extraction of low-dimensional models from multidimensional data. The segmentation method is applied to event-related potentials and fields and early auditory evoked potentials and extracts ERP- and ERF-components and early auditory waves objectively and independent from the number of segments. Additionally, the early auditory wave P_a is modeled by a two-dimensional system of ordinary differential equations. We find a common topology of wave P_a, which lets us conjecture intrinsic low-dimensional underlying attractors in the corresponding neuronal dynamics.

Human performance is strongly influenced by the sequence of events. Decreasing the response-stimulus interval (RSI) between events qualitatively changes these so-called sequential effects. Using event-related brain potentials (ERPs) to detect electrical brain activity related to sequential patterns helps to uncover mechanisms underlying the observed performance data. Using a spatial compatible two-choice task ERPs were recorded from 32 electrode sites and Independent Component Analysis (ICA) applied to separate sequence-sensitive ERP components from two experiments, involving different RSIs. Independent Component Analysis was able to separate temporally and spatially overlapping ERP components. Sensitivity to the sequence of preceding events could be revealed in an early subcomponent of the N100 complex. Moreover, and in line with earlier reports sequential effects were also observed in P300 subcomponents.

We discuss a notion of information processing in brain and behavioral dynamics, in particular the processing of meaningful information, which is testable by means of an experimental coordination and transition paradigm. Two hypotheses on the existence and persistence of mappings between the dynamics of behavioral and brain signals are formulated. A mathematical foundation for the first hypothesis is suggested by means of Volterra integral expansions and by means of excitable systems. Brain signals are captured as cortical currents, as well as the resulting scalp topographies, such as electroencephalograms (EEG) and magnetoencephalograms (MEG). Experimental evidence is provided to support the hypothesis on the existence of such spatiotemporal mappings between behavioral and brain signals.

In this note we describe a simple method for visualizing time-dependent similarities and dissimilarities between the components of a high-dimensional time series. On the base of symbolic dynamics, the time series is turned into a series of matrices whose rows quantify pattern types in the components of the original series. For different scales we introduce distances between the components via the obtained pattern type distributions and approximate them in a one-dimensional manner. The method is illustrated for 19-channel EEG data.

In the present work, we provide new arguments and data indicating that early ERP components are generated at least in part by evoked theta and alpha oscillations. We proceed from the general hypothesis, originally proposed by Erol Basar that ERP's are generated by a superposition of evoked oscillations with different frequencies. Based on findings about event-related desynchronization/synchronization (ERD/ERS), we analyze the following specific hypotheses. If evoked theta and alpha oscillations contribute to the generation of ERP components and if their functional role, type of reactivity and frequency specificity are similar to those of event-related oscillations (measured by ERD/ERS), we expect (i) to see the same functional relationship between frequency and cognitive processes, (ii) the same type of "reactivity" and a (iii) dependency of latency measures of evoked components on IAF. By reviewing respective data, we demonstrate that similar to research about event-related oscillations, evoked alpha reflects attention, whereas evoked theta reflects working memory processes. Furthermore, it was found that individual alpha frequency (IAF) has a significant influence on P1 latency in particular. For a better understanding of these findings, we outline a new theoretical framework. We assume that the P1–N1 complex is generated by an interplay between the synchronous activation of three neuronal network systems, a working memory, attentional, and semantic memory system, each operating with a different frequency, the first in the theta (about 6 Hz), the second in the lower alpha (about 8 Hz) and the third in the upper alpha (about 12 Hz) frequency range. The implications of this theoretical framework are discussed by reviewing research using phase sensitive measures to analyze "local" and "large scale" integration processes between different neural networks.

We present a systematic and straightforward approach to the problem of single-trial classification of event-related potentials (ERP) in EEG. Instead of using a generic classifier off-the-shelf, like a neural network or support vector machine, our classifier design is guided by prior knowledge about the problem and statistical properties found in the data. In particular, we exploit the well-known fact that event-related drifts in EEG potentials, albeit hard to detect in a single trial, can well be observed if averaged over a sufficiently large number of trials. We propose to use the average signal and its variance as a generative model for each event class and use Bayes' decision rule for the classification of new and unlabeled data. The method is successfully applied to a data set from the NIPS*2001 Brain–Computer Interface post-workshop competition. Our result turned out to be competitive with the best result of the competition.

The study of instabilities in perception has attracted much interest in recent decades. The investigations presented here focus on electrophysiological correlates of orientation reversals of both ambiguous visual stimuli and alternating nonambiguous stimuli, representing the two options of the ambiguous version. Based on a refined experimental setup, significant features in the event-related potentials associated with the perception of orientation reversal were found in both cases. Their occipital location, their early occurrence (200–250 ms), and their latency difference (50 ms) offer interesting perspectives for an understanding of unstable brain states in terms of basic concepts of dynamical systems.

We review a neural network model based on chaotic dynamics [Babloyantz & Lourenço, 1994, 1996] and provide a detailed discussion of its biological and computational relevance. Chaos can be viewed as a "reservoir" containing an infinite number of unstable periodic orbits. In our approach, the periodic orbits are used as coding devices. By considering a large enough number of them, one can in principle expand the information processing capacity of small or moderate-size networks. The system is most of the time in an undetermined state characterized by a chaotic attractor. Depending on the type of an external stimulus, the dynamics is stabilized into one of the available periodic orbits, and the system is then ready to process information. This corresponds to the system being driven into an "attentive" state. We show that, apart from static pattern processing, the model is capable of dealing with moving stimuli. We especially consider in this paper the case of transient visual stimuli, which has a clear biological relevance. The advantages of chaos over more regular regimes are discussed.

We present new measures of complexity and their application to event-related potential data. The new measures are based on structures of recurrence plots and makes the identification of chaos–chaos transitions possible. The application of these measures to data from single-trials of the Oddball experiment can identify laminar states therein. This offers a new way of analyzing event-related activity on a single-trial basis.

Recently blind source separation (BSS) methods have been highly successful when applied to biomedical data. This paper reviews the concept of BSS and demonstrates its usefulness in the context of event-related MEG measurements. In a first experiment we apply BSS to artifact identification of raw MEG data and discuss how the quality of the resulting independent component projections can be evaluated. The second part of our study considers averaged data of event-related magnetic fields. Here, it is particularly important to monitor and thus avoid possible overfitting due to limited sample size. A stability assessment of the BSS decomposition allows to solve this task and an additional grouping of the BSS components reveals interesting structure, that could ultimately be used for gaining a better physiological modeling of the data.

Cognitive processes are highly dynamic processes concatenating different components of human thinking successively or parallel in time. Thereby, different cortical networks are generated, transient or stable in time. One important integration mechanism between different cortical sites is the synchronization of electrical oscillations of neural ensembles. Prior studies have shown that instantaneous EEG coherence analysis is a useful tool to unhide transient synchronization phenomena (see e.g. [Krause et al., 1998; Miltner et al., 1999; Schack et al., 1999a, 1999b]). In those studies instantaneous coherence was investigated for selected short time intervals, respectively, specific time parameters of instantaneous coherence were examined.

The present study proposes a method for the evaluation of the whole cognitive process on the basis of instantaneous coherence without loss of time and process information. To this purpose prototypical microstates of synchronous oscillations are constructed. Their temporal, sequential and topographical properties reflect the underlying process of the dynamic activation and deactivation of neuronal networks during information processing. The sequence of microstates may be understood as the orderly arrangement of words of an alphabet in the correspondent thinking process.

The presented method is applied to an event-related cognitive task of comparing categorization processes, pattern comparison, and to an irreproducible long task when solving mathematical problems. In both cases we obtain detailed information about temporal structures and strategies of human thinking.

We present an entropy and complexity analysis of intracranially recorded EEG from patients suffering from a left frontal lobe epilepsy. Our approach is based on symbolic dynamics and Shannon entropy. In particular, we will discuss the possibility to monitor long-term dynamical changes in brain electrical activity. This might offer an alternative approach for the analysis and more fundamental understanding of human epilepsies.

Binocular rivalry is a useful experimental paradigm to investigate aspects of neocortical dynamics related to conscious perception. Frequency-tagged EEG responses to a sine-flickered visual stimulus were contrasted between episodes of perceptual dominance, i.e. conscious perception of that stimulus and perceptual nondominance, i.e. conscious perception of a rival stimulus presented at a different frequency to the other eye. The amplitude and phase distribution of the stimulus-evoked steady-state responses depended on the stimulus modulation frequency, consistent with the presence of global resonance phenomena. At the apparent global resonance frequency, conscious perception of the stimulus modulated the steady-state response over the entire array of electrodes. These effects were significant at electrodes far from the primary visual cortex, including temporal, central, and frontal electrodes. The phase structure of the steady-state response was also investigated using coherence measures. Coherence between electrodes mostly increased during conscious perception of the stimulus. Analysis of partial coherence, removing stimulus-locked responses, indicated that synchronization of each signal to the stimulus flicker at each electrode and synchronization between signals that vary with respect to the stimulus flicker at each electrode both contribute to observed increases in coherence during conscious perception. These distinct modes of synchronization may reflect two different physiological mechanisms by which sensory signals are integrated across the cerebral cortex during conscious experience.

The mammalian retina extracts a set of 12 different "movies" from the visual scene and send each movie to higher visual centers. These movies exist in physically distinct strata of the inner retina, embodied in the dendritic arborizations of a dozen different ganglion cell types. The dendritic arbors are stacked in discrete layers throughout the inner retina where they are synaptically contacted by excitatory and inhibitory connections from a variety of different cell types. This paper outlines the synaptic and physical structure of these layers, and follows the image of a face through the retina from photoreceptors to final output, graphically displaying the transformations that take place as the image is processed by different neural structures.

The interaction of large populations of neurons gives rise to electrical events in the brain, which can be observed at several spatial scales. We show that mutually consistent explanations and simulation of experimental data can be achieved for cortical gamma activity, synchronous oscillation, and the main features of the EEG power spectrum including the cerebral rhythms, and evoked potentials. These simulations include consideration of dendritic and synaptic dynamics, AMPA, NMDA and GABA receptors, and intracortical and cortical/subcortical interactions.

The dynamic properties exhibited in the simulations, Hebbian synaptic modification regulated by a limited set of innate "reward" mechanisms, and infomax principles, can be combined to yield an explanation of elementary adaptive learning.