Stable Irregular Dynamics in Complex Neural Networks

Details Stable Irregular Dynamics in Complex Neural Networks Stable Irregular Dynamics in Complex Neural Networks

2007-05-22

arxiv.org/abs/0705.3214v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

10 pages, 2 figures

Scientific paper

10.1103/PhysRevLett.100.048102

For infinitely large sparse networks of spiking neurons mean field theory shows that a balanced state of highly irregular activity arises under various conditions. Here we analytically investigate the microscopic irregular dynamics in finite networks of arbitrary connectivity, keeping track of all individual spike times. For delayed, purely inhibitory interactions we demonstrate that the irregular dynamics is not chaotic but rather stable and convergent towards periodic orbits. Moreover, every generic periodic orbit of these dynamical systems is stable. These results highlight that chaotic and stable dynamics are equally capable of generating irregular activity.

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