Nonlinear dynamics and statistical physics of excitable systems
Kurrer, Christian Martin
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https://hdl.handle.net/2142/28664
Description
Title
Nonlinear dynamics and statistical physics of excitable systems
Author(s)
Kurrer, Christian Martin
Issue Date
1994
Doctoral Committee Chair(s)
Schulten, Klaus J.
Department of Study
Physics
Discipline
Physics
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
neuronal information coding
excitable systems
neurons
Language
en
Abstract
In the search for the mechanisms of neuronal information coding, attention has recently shifted towards the possible role of neuronal firing correlation. The present thesis addresses the question of how coupled neuronal systems synchronize. Neurons can be described as dynamical systems through the Bonhoeffer-Van der Pol equations. The Bonhoeffer-Van der Pol equations yield either excitable system behavior or oscillator dynamics, depending on a control parameter. Since the neurons are microscopic objects in a fluctuating environment, it is important to add noise to the Bonhoeffer-Van der Pol dynamics in order to achieve a realistic description of neuronal behavior.
Our aim is to understand how the dynamical properties of an ensemble of coupled noisy dynamical systems depend on the properties of its constituents and on the coupling between these constituents. Our calculations and simulations describe two different transitions between phases with uncorrelated neuronal firing and with synchronous neuronal firing. The dynamical system which we investigate is of a very general nature and its study therefore allows us to draw some general conclusions. First, as far as dynamical systems are concerned, the study leads to a reappraisal of the role of Hopf bifurcations in the emergence of limit cycles
in stochastic dynamical systems. Second, as far as neuronal systems are concerned, our investigations indicate that firing synchronicity is fairly common in a large variety of neuronal systems, and draw the attention to the change of firing frequency that accompanies the synchronization
transition.
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