Adaptation controls synchrony and cluster states of coupled threshold-model neurons.
We analyze zero-lag and cluster synchrony of delay-coupled nonsmooth dynamical systems by extending the master stability approach, and apply this to networks of adaptive threshold-model neurons. For a homogeneous population of excitatory and inhibitory neurons we find (i) that subthreshold adaptation stabilizes or destabilizes synchrony depending on whether the recurrent synaptic excitatory or inhibitory couplings dominate, and (ii) that synchrony is always unstable for networks with balanced recurrent synaptic inputs. If couplings are not too strong, synchronization properties are similar for very different coupling topologies, i.e., random connections or spatial networks with localized connectivity. We generalize our approach for two subpopulations of neurons with nonidentical local dynamics, including bursting, for which activity-based adaptation controls the stability of cluster states, independent of a specific coupling topology.
Institut für Softwaretechnik und Theoretische Informatik, Technische Universität Berlin, Marchstraße 23, 10587 Berlin, Germany and Bernstein Center for Computational Neuroscience Berlin, Philippstraße 13, 10115 Berlin, Germany.
Josef
J
Ladenbauer
Judith
J
Lehnert
Hadi
H
Rankoohi
Thomas
T
Dahms
Eckehard
E
Schöll
Klaus
K
Obermayer
D000222:Adaptation, Physiological; D008564:Membrane Potentials; D008959:Models, Neurological; D009415:Nerve Net / Q000166:cytology* / Q000502:physiology; D009474:Neurons / Q000166:cytology*