title: Stable irregular dynamics in complex neural networks.
abstract: Irregular dynamics in multidimensional systems is commonly associated with chaos. 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 any irregular dynamics that characterizes the balanced state is not chaotic but rather stable and convergent towards periodic orbits. These results highlight that chaotic and stable dynamics may be equally irregular.
authors: Network Dynamics Group, Max Planck Institute for Dynamics & Self-Organization (MPIDS), Göttingen, Germany.
authors: Sven
authors: S
authors: Jahnke
authors: Raoul-Martin
authors: RM
authors: Memmesheimer
authors: Marc
authors: M
authors: Timme
mesh_terms: D008959:Models, Neurological; D009415:Nerve Net / Q000502:physiology*; D009433:Neural Inhibition; D009474:Neurons / Q000502:physiology; D017711:Nonlinear Dynamics