Nonlinear dynamics and statistical physics of excitable systems

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Year dc:date

2012

Author dc:creator

• Kurrer, Christian Martin

Contributors dc:contributor

• Schulten, Klaus J.

• neuronal information coding
• excitable systems
• neurons

Statement dc:rights

• 1994 Christian Martin Kurrer

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/28664

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/28664