Regensburg 2007 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 2: Time-delayed feedback and neural networks

DY 2.5: Talk

Monday, March 26, 2007, 11:30–11:45, H3

Stable Irregular Dynamics in Complex Neural Networks — •Sven Jahnke, Raoul-Martin Memmesheimer, and Marc Timme — Network Dynamics Group, Max Planck Institute for Dynamics and Self-Organization, and Bernstein Center for Computational Neuroscience (BCCN), Bunsenstrasse 10, 37073 Göttingen

Models mimicking the ’ground state’ of neural networks in the cortex exhibit highly irregular spiking dynamics of individual neurons and weak cross-correlations between the neurons. In their mean field study v.Vreeswijk and Sompolinsky (Science, 1996) suggest that this irregular dynamics in general is chaotic.

Here we investigate this irregular dynamics in finite networks keeping track of all individual spike times. For delayed, purely inhibitory interactions we give strong evidence that the irregular dynamics is not chaotic but in fact stable and convergent towards periodic orbits.

Moreover, we show that every generic periodic orbit of these dynamical systems is stable. These results indicate that chaotic and stable dynamics are equally capable of generating irregular neuronal activity. We investigate possible transitions to chaotic dynamics by changing features of the neurons and their interactions.