Biology – Quantitative Biology – Neurons and Cognition
Scientific paper
2005-10-25
Chaos 16, 015108 (2006)
Biology
Quantitative Biology
Neurons and Cognition
17 pages, 12 figures, submitted to Chaos
Scientific paper
10.1063/1.2150775
We analyze the dynamics of networks of spiking neural oscillators. First, we present an exact linear stability theory of the synchronous state for networks of arbitrary connectivity. For general neuron rise functions, stability is determined by multiple operators, for which standard analysis is not suitable. We describe a general non-standard solution to the multi-operator problem. Subsequently, we derive a class of rise functions for which all stability operators become degenerate and standard eigenvalue analysis becomes a suitable tool. Interestingly, this class is found to consist of networks of leaky integrate and fire neurons. For random networks of inhibitory integrate-and-fire neurons, we then develop an analytical approach, based on the theory of random matrices, to precisely determine the eigenvalue distribution. This yields the asymptotic relaxation time for perturbations to the synchronous state which provides the characteristic time scale on which neurons can coordinate their activity in such networks. For networks with finite in-degree, i.e. finite number of presynaptic inputs per neuron, we find a speed limit to coordinating spiking activity: Even with arbitrarily strong interaction strengths neurons cannot synchronize faster than at a certain maximal speed determined by the typical in-degree.
Geisel Theo
Timme Marc
Wolf Fred
No associations
LandOfFree
Speed of synchronization in complex networks of neural oscillators Analytic results based on Random Matrix Theory does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Speed of synchronization in complex networks of neural oscillators Analytic results based on Random Matrix Theory, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Speed of synchronization in complex networks of neural oscillators Analytic results based on Random Matrix Theory will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-430380