Journal
JOURNAL OF MATHEMATICAL BIOLOGY
Volume 56, Issue 3, Pages 311-345Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s00285-007-0117-3
Keywords
neural networks; dynamical systems; symbolic coding
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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.
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