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R M Borisyuk

Publications and source records attributed to R M Borisyuk.

5 recordsLinked to original sources

Information coding on the basis of synchronization of neuronal activity.

Three types of oscillatory neural networks are considered and their dynamics are analyzed. The regime of chaotic coherent oscillations was found in a network of excitatory and inhibitory integrate-and-fire neurons with all-to-all connections. The regime of envelope oscillations was found in a chain of neural oscillators with local connections. The regime of partial synchronization of the central element with a group of peripheral oscillators under perturbation of the rest of the peripheral oscillators was found in the oscillatory neural network of phase oscillators. A possible use of the dynamical regimes for the information coding and processing is briefly discussed.

Models, Biological

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

In this paper we present an oscillatory neural network composed of two coupled neural oscillators of the Wilson-Cowan type. Each of the oscillators describes the dynamics of average activities of excitatory and inhibitory populations of neurons. The network serves as a model for several possible network architectures. We study how the type and the strength of the connections between the oscillators affect the dynamics of the neural network. We investigate, separately from each other, four possible connection types (excitatory-->excitatory, excitatory-->inhibitory, inhibitory-->excitatory, and inhibitory-->inhibitory) and compute the corresponding bifurcation diagrams. In case of weak connections (small strength), the connection of populations of different types lead to periodic in-phase oscillations, while the connection of populations of the same type lead to periodic anti-phase oscillations. For intermediate connection strengths, the networks can enter quasiperiodic or chaotic regimes, and can also exhibit multistability. More generally, our analysis highlights the great diversity of the response of neural networks to a change of the connection strength, for different connection architectures. In the discussion, we address in particular the problem of information coding in the brain using quasiperiodic and chaotic oscillations. In modeling low levels of information processing, we propose that feature binding should be sought as a temporally coherent phase-locking of neural activity. This phase-locking is provided by one or more interacting convergent zones and does not require a central ¿top level¿ subcortical circuit (e.g., the septo-hippocampal system). We build a two layer model to show that although the application of a complex stimulus usually leads to different convergent zones with high frequency oscillations, it is nevertheless possible to synchronize these oscillations at a lower frequency level using envelope oscillations. This is interpreted as a feature binding of a complex stimulus.

Animals

In-phase and antiphase self-oscillations in a model of two electrically coupled pacemakers.

The dynamic behavior of a model of two electrically coupled oscillatory neurons was studied while the external polarizing current was varied. It was found that the system with weak coupling can demonstrate one of five stable oscillatory modes: (1) in-phase oscillations with zero phase shift; (2) antiphase oscillations with half-period phase shift; (3) oscillations with any fixed phase shift depending on the value of the external polarizing current; (4) both in-phase and antiphase oscillations for the same current value, where the oscillation type depends on the initial conditions; (5) both in-phase and quasiperiodic oscillations for the same current value. All of these modes were robust, and they persisted despite small variations of the oscillator parameters. We assume that similar regimes, for example antiphase oscillations, can be detected in neurophysiological experiments. Possible applications to central pattern generator models are discussed.

Animals

Bifurcation analysis of a neural network model.

This paper describes the analysis of the well known neural network model by Wilson and Cowan. The neural network is modeled by a system of two ordinary differential equations that describe the evolution of average activities of excitatory and inhibitory populations of neurons. We analyze the dependence of the model's behavior on two parameters. The parameter plane is partitioned into regions of equivalent behavior bounded by bifurcation curves, and the representative phase diagram is constructed for each region. This allows us to describe qualitatively the behavior of the model in each region and to predict changes in the model dynamics as parameters are varied. In particular, we show that for some parameter values the system can exhibit long-period oscillations. A new type of dynamical behavior is also found when the system settles down either to a stationary state or to a limit cycle depending on the initial point.

Biological Clocks

A new statistical method for identifying interconnections between neuronal network elements.

A new method is proposed to analyse dependencies in point processes, which takes into account specific character of neuronal activity. Simulation modelling of neuronal network revealed that the estimated weight of connection depends monotonically on the value of the model synaptic strength. In contrast to the crosscorrelation, the method allows for nonlinear interconnections and does not require point processes to be stationary and samples to be large. Examples are presented of the method's application to neurophysiological data analysis.

Animals