# Нелинейная динамика и нейронаука

## Oscillatory instability and spontaneous subthreshold oscillations in a network of diffusively coupled calcium oscillators

The paper is devoted to the investigation of the dynamics of a network of interacting astrocytes. The astrocytes represent brain glial cells capable to generate chemical activity signals (calcium pulses). Similarly to nerve cells (neurons) the astrocytes form networksof interacting units coupled by means of gap junctions. The junctions represent special protein channels providing the di?usion of chemically active species between neighboring cells.

## A neural network as a predictor of the discrete map

The possibility of predicting the regular and chaotic dynamics of a discrete map by using artificial neural network is studied. The method of error backpropagation is used for calculation the coefficients of the multilayer network. The predicting properties of the neural network are explored in a wide region of the system parameter for both regular and chaotic behaviors. The dependance of the prediction accuracy from the degree of chaos and from the number of layers of the network is studied.

## The phenomenon of self-referential phase reset in ensembles of interacting fitzhugh–nagumo neurons

The phenomenon of self-referential phase reset are investigated in ensembles of interacting FitzHugh–Nagumo neurons with di?erent topology of couplings. It is shown that the reset phase of neurons oscillation is independent of the initial phase and is de?ned by the stimulus parameters. This process does not require direct in?uence on all elements of the ensemble and takes place when stimulus is applied to one of the interacting neurons only. The in?uence of inter-neuron couplings and stimulus parameters on ensemble dynamics and phase reset phenomenon is studied.

## Regular and chaotic oscillations in astrocyte model with regulation of calcium release kinetics

The dynamics of an astrocyte model is investigated. The astrocytes represent a type of glial cells regulating oscillations of major signaling cells, e.g. neurons. Subserved by complex molecular mechanisms the astrocytes generate calcium auto-oscillations which, in turn, are associated with the release of neuroactive chemicals into extracellular space. At variance with classical astrocyte models the three-component model considered takes into account a regulation of calcium release due to nonlinear dynamics of inositol-1,4,5 trisphosphate (IP3).

## Feature of simultaneous influence of excitatory synaptic currents on a neuron with differential responses

The simultaneous influence of excitatory synaptic stimuli (the tonic AMPA and NMDA currents) on the neuron model with response differentiation is studied. It is shown that different types of neuron activity (rest state, low frequency or high frequency firing) are observed depending on the conductance of the AMPA and NMDA receptors. It is found that for the certain parameters values if both types of receptors are activated simultaneously, it is possible to obtain maximal frequency to be approximately 20% greater than that with the NMDA current alone.

## Alternative methods for spiral wave chaos control and suppressing in cardiac models

We investigate elements, which describes the Luo–Rudy model equations. We ana?lyze the influence of different parameters for the spiral wave chaos properties.We analyze the effect of (i) constant current influence, (ii) calcium channels blocking, (iii) potassium channels activating. We present the histograms of the middle frequencies of elements, when the spiral wave chaos takes place.

## Dynamics of a network of interacting phase oscillators with dynamic couplings

We investigate dynamical states formed in a network of coupled phase oscillators in which strength of interactions between oscillators evolve dynamically depending on their relative phases. The feature of the system is co-evolution of coupling weights and states of elements. It is ascertained that depending on the parameters the network exhibit several types of behavior: globally synchronized state, two-cluster and multi-cluster states, various synchronized states with a fixed phase relationship between oscillators and desynchronized state. Download full version

## Macroscopic model of visual processing in brain structures in normal condition and description of the transition to epileptiform regime

This paper presents the functional model of signal processing in networks of similar interconnected active elements. On the one hand, it is a macroscopic model of the dynamic interactions between neural networks and its states can be considered as normal and abnormal modes of signal processing (for example, images). On the other hand, the model and the calculation results can be considered as a variant of modeling epilepsy. In this paper we develop an information macroscopic approach to the modeling of epilepsy, which in this sense is unique. Download full version

## Research of dynamic modes in the mathematical model of elementary thalamocortical cell

In the work the mathematical model of the thalamocortical network’s unit cell and it’s characteristic dynamical modes in system, describing the interaction between a thalamus, thalamus reticular nucleus and a cortex, is studied. During normal information processing, input signal gating occurs in time in the thalamo-cortical network. The violation of the normal functioning leads to an epilepsy, when the perception of information is disrupted.

## Mathematics of mind

In this slide-lecture we formulate a novel paradigm for the mathematical description of mental functions such as consciousness, creativity, decision making and prediction of the future based on the past. Such cognitive functions are described in the framework of canonical nonlinear dynamical models that form joint global hierarchical networks. Subnetworks cooperate and compete with each other by inhibition.

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