Nonlinear Dynamics and Neuroscience

Universal models of neuron­like type, from which the systems of transformation and identification of information signals are constructed in accordance with pre­determined goals are considered. The models of different levels in a model system are aimed at performing functional operations characteristic of live systems. The presented set of base models and the most obvious dynamic modes of their operation can adequately describe the features of conscious perception and response of live systems to various sensor signals.

Now models (simulators) of neural networks are actively developed. Their architecture and design are based on features of structure and principles of work of real neurons and neurobiological systems. Working out neurolike models based on the data about architecture of connections in a brain, it is aimed at finding­out of principles of work of its neural structures. In experimental researches it is revealed that interconnected neuronal modules such as cortex, reticular modules of thalamus, specific thalamus play the important role in processes of information processing.

It is shown that discovered fractal properties of neuronal interspike interval sequence contradicts the reflex theory. The simplified model of formation and realization of individual experience based on reflex theory view of individual experience structure as a tree has been proposed. Behavior of the model does not show fractal properties. It is suggested that non­reflex model of individual experience structure formed as a tree of skills is needed. It is shown the possibility of nonlinear (fractal) properties estimation in the data for evaluation of a theory.

The conceptual model and computer simulations results of path integration in free­scalable nonlinear oscillator neural networks with even cyclic inhibition (ECI­networks) are discussed in this paper. To estimate the phase shifting under input impact the ECI­networks contain two subsystems namely reference and information ones. The population of reference (nonencoding) oscillatory units has significant role in generation and stabilization of numerous time scales despite it don’t assist directly in the phase pattern encoding of input signals.

The results of neurophysiological and modeling studies focused on activity synchronization among of different types of neurons and spike shape dynamics in two bistability transition states have been presented. In modeling study, spike duration range of «fast» or «slow» neurons recorded in neurophysiological experiments were simulated.

The work is devoted to quantitative modelling of regularities in the subjective comparison of the significance of unlike material and mental objects which are of a substantial value for a man. It is assumed that each object is perceived by a man as a complex semantic stimulus characterized by subjective significance and a finite set of the features which are to be taken into account.

Use of phase-locked loop as a model of neuron-like element is discussed. Parameter space of the model is partitioned into areas of different regimes specific for dynamics of real neurons. Bifurcation mechanisms of transitions between regimes are examined.

We investigated bifurcation mechanisms of oscillatory dynamics of interacting chemically excitable cells (astrocytes). In model of three interacting astrocytes we studied bifurcation transitions leading to generation of calcium oscillations induced by the intercellular diffusion. We analyzed basic mechanisms of limit cycle instabilities and destructions, typical transitions to chaotic oscillations and basic properties of intercellular synchronization.

Bifurcation mechanisms of oscillatory dynamics in a biophysical model of chemically excitable brain cells (astrocytes) were analyzed. In contrast to neuronal oscillators widely studied in nonlinear dynamics the astrocytes do not possess electrical excitability but capable to generate chemical oscillations which modulate neuronal signaling. Astrocyte dynamics is described by third-order system of ordinary differential equations derived from biophysical kinetics.

Method for detecting of two different types of sleep spindles on electroencephalogram was offered. High precision of this method was demonstrated; it can be used in neurophysiological research of regularity of appearing of different patterns on electroencephalogram.