Nonlinear Dynamics and Neuroscience

We study synchronization in ensembles of locally diffusive coupled Bonhoeffer–van der Pol oscillators. Individual elements frequencies influence on excitation propagation in one- and two-dimensional media is investigated. We show that excitation propagation speed depends on frequency mismatch between synchronization frequency and elements’ individual frequencies. Qualitative and quantitative results describing this effect are numerical modeling data and analytical research.

The problem of compact mathematical model reconstruction of short electroencephalogram tracings during epileptic seizure is solved. This kind of model map can be useful in many applications, for example, in time series segmentation with following clustering of obtained fragments. Optimization methods are proposed as a solution. It is shown that application of optimization methods allows to obtain adequate model at that time decreasing number of modeling map basis functions.

A new model of neurons like elements is suggested in the paper. The model is based on the generalized Lottka–Volterra model with excitatory coupling. The study is motivated by the fact that the excitatory couplings are the dominating type of interactions between neurons in the human brain. It is shown in the paper that there are two regimes exist in such ensemble of oscillators in dependence on the coupling between the elements: the regime with stable heteroclinical cycle and the regime with stable limit cycle.

Switching activity in the ensemble of inhibitory coupled Poicare systems is considered. The existence of heteroclinic contour in the phase space at the certain domain of parameter space has shown.

Dynamics of the ensemble of non-identical inhibitory and diffusively coupled systems of Poincare is considered. The approximate bifurcation diagrams for all qualitatively different regimes of the network activity have shown. There are areas of the parameter space corresponding to different dynamic regimes, such as multistability, extinction, modulation, bursting and synchronization.

In the work we consider the classic cyclic schemes for the construction of cognitive processes. Based on neurobiological data we indicate the need to introduce a special mechanism for adaptive control signals of a mismatch in cognitive processes at the stage preceeding the decision point. Endogenous opioid system can be considered one of the major neurochemical candidates for such «breakers». This system provides the suppression of signals about a mismatch between current and target states of the cognitive system.

The process of a problem area experts knowledge acquisition is considered from a nonlinear dynamics positions. Stages and types of acquired knowledge are marked out; the role of an intuitive thinking in decision process concerning complex objects is defined. The role of intelligent data analysis methods in new knowledge forming processes is defined. The result of a developed «Semantic computer knowledge base analysis» algorithm is given on an example of the concrete medical problem.

Through the development of methods for detecting the dynamics of spatial­temporal patterns of activity in the nervous system fundamental evidences obtained, that the sensory code have integrative nature and theories of localisation of function are inconsistent. The paper presents a review of electrophysiological data and models, indicating the integrative mechanisms of information coding in the peripheral skin analyzer of humans and animals.

We propose a version of the neuroprocessor construction scheme, which in principle capable to solve problems commonly treated as creative work. The role of conventional information is discussed, and the specific block for the symbol formation is suggested. The system capable to solve logic problems has been pointed out. It is shown that the symbol (logical) subsystem is able to interpolate and extrapolate in the process of pattern recognition and prognosis.

The concepts of «pattern» and «symbol» and their functions are discussed in the context of «thinking» system of combined neuroprocessors. It is shown that the pattern subsystem does play a key role in recording and store of information. The symbol subsystem initiation provides the transition to conventional semantic information and communications with environment. The paradigm of attention within the scheme presented is secured by a parametric effect of symbol subsystem on the image one.