Nonlinear Dynamics and Neuroscience

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

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 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 diffusion of chemically active species between neighboring cells.

It is possible or not using formulas to penetrate the most intimate sphere of human cognitive functions – his creative laboratory. After all, even the air in this sphere filled with ambiguity and  improvisation. In the last three-five years, such attempts are verysuccessfully taken by the  physiologists, psychologists and experts in nonlinear physics. In this article we look at two examples  of creative processes – writing poems and jazz improvisation. From a mathematical point of view,  these processes have much in common and are based on universal principles of mental dynamics.

Serotonin is a key modulator of neuronal activity both at the system level and at the level of local (short­range) interactions. However, in contrast to the synaptically connected neuron ensembles, there are much less qualitative models that describe the serotonin­controlled neural circuits.

The EEG research technique on the basis of autoregressive models construction and Granger causality estimation by experimental data are described in this article. The EEG is written down from the brain of WAG/Rij rats, which are absence-epilepsy contaminated. The EEG episodes well enough described in terms of small order linear display along with the episodes with expressed nonlinearity are revealed during the analysis. The EEG episodes ordering is spent in accordance with the model parameters received and physio-logical condition of the animals.

The detailed wavelet analysis of sleep electric brain activity, obtained from rats with genetic predisposition to absence-epilepsy, has been performed. Characteristic features of time-and-frequency structure of sleep spindles (oscillatory pattern, that serve as electroencephalographic correlate for slow-wave sleep) have been discovered in long-term electroencephalographic data. Operation has been performed using continuous wavelet transform.

The paper summarizes the main results of analysis of electroencephalograms in rats with genetic predisposition to absence epilepsy (WAG/Rij rat strain). Properties of epileptic activity are described in time and in frequency domains; dynamics of epileptic activity is investigated, as well as changes in electroencephalogram structure prior to epileptic discharges. Physiologic interpretation of the investigated phenomena helps in better understanding of the nature of the investigated phenomena.

We propose a new method for analysis of electroencephalograms. It is based on construction of a parameterized stochastic model of the observed process (evolution operator). A certain functional form of the evolution operator is proposed. This form describes deterministic properties of the investigated process, as well as stochastic ones. The parameters of the evolution operator are reconstructed from the experimental data by using the Bayesian approach. New («fast») dynamical variables, which allow for the peculiar features of electroencephalogram, are found.

This paper presents the approaches and methods for modeling and analysis of the open human cerebral cortex IR­thermo maps. The main goal of the development is to solve fundamental problems: the selection of reliable informative features, which allow detecting abnormalities of the brain, to classify its types, and to delineate its boundaries. The created analytical tools are also directed to the studying fundamental problems related to the mechanisms of autoregulation and compensation in the brain. The described methods and approaches were tested on the real medical history.