Using the concepts of chaotic dynamical systems, we present an interpretation of dynamic neural activity found in cortical and subcortical areas. The discovery of chaotic itinerancy in high-dimensional dynamical systems with and without a noise term has motivated a new interpretation of this dynamic neural activity, cast in terms of the high-dimensional transitory dynamics among "exotic" attractors. This interpretation is quite different from the conventional one, cast in terms of simple behavior on low-dimensional attractors. Skarda and Freeman (1987) presented evidence in support of the conclusion that animals cannot memorize odor without chaotic activity of neuron populations. Following their work, we study the role of chaotic dynamics in biological information processing, perception, and memory. We propose a new coding scheme of information in chaos-driven contracting systems we refer to as Cantor coding. Since these systems are found in the hippocampal formation and also in the olfactory system, the proposed coding scheme should be of biological significance. Based on these intensive studies, a hypothesis regarding the formation of episodic memory is given.

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Toward an interpretation of dynamic neural activity in terms of chaotic dynamical systems

We discuss the conversion of the description of the dynamics of a neural network from a temporal variation of synaptic currents driven by point spikes and modulated by a synaptic structure to a description of the current dynamics driven by spike rates. The conditions for the validity of such a conversion are discussed in detail and are shown to be quite realistic in cortical conditions. This is done in preparation for a discussion of a scenario of an attractor neural network, based on the interaction of synaptic currents and neural spike rates.The spike rates are then expressed in terms of the currents themselves to provide a closed set of dynamical equations for the currents. The current-rate relation is expressed as a neuronal gain function, converting currents into spike rates. It describes an integrate-and-fire element with noisy inputs, under explicit quaniitatve conditions which we argue to be plausible in a cortical situation In particular, it is shown that the gain of the current to rate transduct...

Quantitative study of attractor neural network retrieving at low spike rates: I. substrate—spikes, rates and neuronal gain

Synchronization is a fundamental characteristic of complex systems and a basic mechanism of self-organization. A traditional, accepted perspective on epileptiform activity holds that hypersynchrony covering large brain regions is a hallmark of generalized seizures. However, a few recent reports have described substantial fluctuations in synchrony before and during ictal events, thus raising questions as to the widespread synchronization notion. In this study, we used magnetoencephalographic recordings from epileptic patients with generalized seizures and normal control subjects to address the extent of the phase synchronization (phase locking) in local (neighboring) and distant cortical areas and to explore the ongoing temporal dynamics for particular ranges of frequencies at which synchrony occurs, during interictal and ictal activity. Synchronization patterns were found to differ somewhat depending on the epileptic syndrome, with primary generalized absence seizures displaying more long-range synchrony in all frequency bands studied (3-55 Hz) than generalized tonic motor seizures of secondary (symptomatic) generalized epilepsy or frontal lobe epilepsy. However, all seizures were characterized by enhanced local synchrony compared with distant synchrony. There were fluctuations in the synchrony between specific cortical areas that varied from seizure to seizure in the same patient, but in most of the seizures studied, regardless of semiology, there was a constant pattern in the dynamics of synchronization, indicating that seizures proceed by a recruitment of neighboring neuronal networks. Together, these data indicate that the concept of widespread "hypersynchronous" activity during generalized seizures may be misleading and valid only for very specific neuronal ensembles and circumstances.

https://www.jneurosci.org/content/jneuro/25/35/8077.full.pdf

Enhanced Synchrony in Epileptiform Activity? Local versus Distant Phase Synchronization in Generalized Seizures

Dynamics and bifurcations of two coupled neural oscillators with different connection types.

A theory of the function of cerebral cortex and thalamus is sketched. 1. Introduction This report sketches the author’s theory of cerebral cortex and thalamus; incorporating relevant discoveries, improvements, changes and updates as of the issue date. The main focus is to provide a coherent, integrated picture of that portion of the theory which provides answers to the following questions: What is cortical knowledge and how is it acquired and stored?, and How is cortical knowledge used to carry out thinking? The theory’s explanation for another key aspect of cortical and thalamic function – the moment-by-moment selection, evaluation, and execution of the action commands that control waking brain activity and muscle movement – is also briefly addressed. This theory proposes the first cogent answers to these questions and therefore should be of interest to both scientists and technologists. In particular, the theory’s characterizations of knowledge and thinking are radically different from the ‘reasoning’ approaches that others have considered; and, given their efficacy (as demonstrated herein via computer thinking experiments), these deserve attention on their own merits. The reader is warned that this theory is not a simple ‘sound bite’ discovery; as is today’s fashion. The pieces of this theory emerged gradually over decades (I began research in computational neurobiology in 1968). However, these pieces only came together as a whole late in 2003. Thus, this report must introduce and relate a number of novel concepts and show how they fit together. To keep the discussion accessible, detailed mathematical models of feature attractors and knowledge links are not discussed. The mathematics of confabulation is so simple that it is included. The basic claim of the theory is that the cerebral cortex and thalamus implement thousands of lexicons, each containing thousands of symbols. These constitute the terms of reference used to describe the objects and actions of the mental universe. Each such lexicon is postulated to be implemented by a single, modular, thalamocortical neuronal circuit called a feature attractor (each symbol of the lexicon is represented by a distinctive population of co-active neurons). Each cortical item of knowledge (of which the average human has billions) is hypothesized to take the form of a unidirectional neuronal linkage between the neurons representing one symbol in one lexicon to neurons representing a second symbol in a second lexicon. Simultaneous inputs from (potentially) thousands of knowledge links to a feature attractor cause many of the neural ensembles representing symbols of its lexicon to become partially excited. The feature attractor then operates; extinguishing all of these excited neurons except those of the single most excited symbol ensemble. This simple, fast, ‘winner-take-all’ information processing operation, termed confabulation, is postulated to be the fundamental mechanism of vertebrate cognition. The next section of this report (derived from a stand-alone article that has not yet been published) discusses an idealized mathematical description of confabulation. This discussion illustrates, largely sans biology, the essence of cortical knowledge acquisition, knowledge storage, and thinking. The third section then overviews how these mechanisms of knowledge storage and confabulation are implemented in biological tissue. This

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V. I. Kryukov

Papers

The metastable and unstable states in the brain