Nonlinear Dynamics and Neuroscience

Topic. In this paper, we investigate the applicability of the known method for detecting the couplings between two oscillators, based on experimental phase dynamics modeling by phases time series in cases where there are several peaks in the signal power spectrum.

Topic. The phenomenological model of ensemble of three neurons coupled by chemical (synaptic) and electrical couplings is studied. Single neuron is modeled by van der Pol oscillator.

In this paper we present the results of investigation of intermittent phase synchronization in a real neurophysiological system. This phenomenon is observed in different systems as well as near the boundaries of various types of chaotic synchronization.

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.

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.

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.

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.

We investigate elements, which describes the Luo–Rudy model equations. We analyze 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.

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.

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).