Biomedical subjects

S Popovych

Publications and source records attributed to S Popovych.

2 recordsLinked to original sources

PubMed2006

Complex dynamics of a single neuron model.

We study a mathematical model of a single neuron with self-coupling. The model is based on the FitzHugh-Nagumo oscillator and an equation describing synaptic properties of the neuron. The analysis of the model is focused on its dynamics, depending on parameters characterizing synaptic time constants and external signals that affect the neuron. Applying Lyapunov exponents and bifurcation analysis, we point out the occurrence of parameter regions with different behavior such as bursting (chaotic or periodic), spiking, and multistable phenomena. Moreover, we can describe the dynamics of the model using an analytical approximation of the one-dimensional Poincaré map extracted from the numerical simulations.

Action Potentials↗

PubMed2000

Chaos-hyperchaos transition

The chaos-hyperchaos transition occurs when the second Lyapunov exponent becomes positive. We argue that this transition is mediated by changes in the stability of an infinite number of unstable periodic orbits embedded in the chaotic attractor. Bifurcations of unstable periodic orbits occur in the neighborhood of the chaos-hyperchaos transition point where we observe unstable variable dimensionality. We give evidence that the chaos-hyperchaos transition is initiated by (i) the saddle-repeller bifurcation of a particular unstable periodic orbit usually of low period, (ii) the appearance of a repelling node in the saddle-node bifurcation, after which the chaotic attractor becomes riddled, or (iii) the absorption of the repeller (unstable node or focus) originally located out of the attractor by the growing attractor.

Journal Article↗