title: A discrete time neural network model with spiking neurons. Rigorous results on the spontaneous dynamics.
abstract: We derive rigorous results describing the asymptotic dynamics of a discrete time model of spiking neurons introduced in Soula et al. (Neural Comput. 18, 1, 2006). Using symbolic dynamic techniques we show how the dynamics of membrane potential has a one to one correspondence with sequences of spikes patterns ("raster plots"). Moreover, though the dynamics is generically periodic, it has a weak form of initial conditions sensitivity due to the presence of a sharp threshold in the model definition. As a consequence, the model exhibits a dynamical regime indistinguishable from chaos in numerical experiments.
authors.affiliation: INRIA, 2004 Route des Lucioles, 06902 Sophia-Antipolis, France. bruno.cessac@inln.cnrs.fr
authors.forename: B
authors.initials: B
authors.lastname: Cessac
mesh_terms: D000200:Action Potentials / Q000502:physiology*; D000465:Algorithms; D017774:Long-Term Potentiation / Q000502:physiology; D036881:Long-Term Synaptic Depression / Q000502:physiology; D008390:Markov Chains; D008564:Membrane Potentials / Q000502:physiology; D008954:Models, Biological; D009415:Nerve Net / Q000502:physiology*; D009473:Neuronal Plasticity / Q000502:physiology; D009474:Neurons / Q000502:physiology*; D013569:Synapses / Q000502:physiology; D009435:Synaptic Transmission / Q000502:physiology