Regensburg 2010 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 15: Reaction Diffusion Systems

DY 15.4: Talk

Wednesday, March 24, 2010, 10:45–11:00, H46

Pattern formation in neuronal ensembles coupled by the external medium — •Nikolaos Kouvaris, Felix Müller, and Lutz Schimansky-Geier — Institute of Physics, Humboldt University of Berlin, Newtonstr. 15, D-12489 Berlin, Germany

The variation of extracellular concentrations can affect the firing activity in neuronal fields. As an example we mention the release of potassium ions that lower the threshold of neurons. This process can influence strongly the behavior of single neurons and of large ensembles. We address this problem by studying simplified excitable units modeled as a FitzHugh - Nagumo system coupled to a third variable describing the exterior. The release of the chemical agent is due to the firing events. That leads to pattern formation in the spatially extended system ranging from spirals and moving clusters to inverted structures. As an abstract modification for the excitable system, we consider a discrete two-state excitable unit. Each state, firing or refractory, is characterized by a waiting time density depending on the external concentrations. We study the dynamics of a single unit embedded in the extracellular medium as well as interacting units in the spatially extended situation. In these models the neuronal interaction is only chemically via the released and diffusing substrate at large time scales. All other neuronal interaction is modeled as noise.

1. D. E. Postnov, F. Müller, R. B. Schuppner and L. Schimansky-Geier, Phys. Rev. E 80, 031921 (2009).

2. T. Prager, M. Falcke, L. Schimansky-Geier and M. Zaks, Phys. Rev. E 76, 011118 (2007).