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Plenary Lecture

Nonlinear Dynamic Systems, Bursting Oscillations of Neurons and Synchronization

Professor Milan Stork
Department of Applied Electronics and Telecommunications
&
RICE - Regional Innovation Centre for Electrical Engineering
University of West Bohemia Plzen
Czech Republic
E-mail: stork@kae.zcu.cz

Abstract: There are several motivations to be interested in fast-slow dynamics. For instance, many physiological or biological systems display different time scales. The bursting oscillations which can be observed in neurons, β-cells of the pancreas and population dynamics are studied and analyzed as fast-slow systems. In lecture a natural generalization to the notion of bursting oscillations where, for instance, the active phase is chaotic and alternates with a quiescent phase. In the first part of the lecture, we introduce dynamics with bursting oscillations based on the Hindmarsh–Rose system and similar bursting systems. Next part describes the bursting chaotic synchronization of two or chain of bidirectional coupled neurons and these systems are simulated since the synchronization of individual neurons is thought to play a key role in Parkinson’s disease, essential tremor, and epilepsies. In next part, the bursting discrete time systems are described and simulated. In the last part external periodic signal is used for neurons synchronization. Such kind of external stimulation of brain has been extensively studied with respect to potential application to the control of pathological rhythms. The dissipativity, instability and stability of the presented systems are also analyzed. The designed systems were simulated and partly constructed in digital versions.

Brief Biography of the Speaker: Milan Stork received the M.Sc. degree in electrical engineering from the Technical University of Plzen, Czech Republic at the department of Applied electronics in 1974. He specialized in electronics systems and control in research institute in Prague. Since 1977 he worked as lecturer on University of West Bohemia in Plzen. He received Ph.D. degree in automatic control systems at the Czech Technical University in Prague in 1985. In 1997, he became as Associate Professor. From 2007 he is full professor at the Department of Applied Electronics and Telecommunication, faculty of electrical engineering on University of West Bohemia in Plzen, Czech Republic. He has numerous journal and conference publications. He is member of editorial board magazine "Physician and Technology". His research interest includes analog/digital linear, nonlinear and chaotic systems, control systems, signal processing and biomedical engineering, especially cardiopulmonary exercise systems. From 2011 he also works in research centre: Regional Innovation Centre for Electrical Engineering (RICE).

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