TY - JOUR
T1 - Phase-locking and bistability in neuronal networks with synaptic depression
AU - Akcay, Zeynep
AU - Huang, Xinxian
AU - Nadim, Farzan
AU - Bose, Amitabha
N1 - Funding Information:
This work was supported, in part, by PSC CUNY 68127-00 46 (ZA), NIH MH060605 (FN) and NSF DMS1122291 (AB).
Funding Information:
This work was supported, in part, by PSC CUNY68127-00 46 (ZA), NIHMH060605 (FN) and NSFDMS1122291 (AB).
Publisher Copyright:
© 2017 Elsevier B.V.
PY - 2018/2/1
Y1 - 2018/2/1
N2 - We consider a recurrent network of two oscillatory neurons that are coupled with inhibitory synapses. We use the phase response curves of the neurons and the properties of short-term synaptic depression to define Poincaré maps for the activity of the network. The fixed points of these maps correspond to phase-locked modes of the network. Using these maps, we analyze the conditions that allow short-term synaptic depression to lead to the existence of bistable phase-locked, periodic solutions. We show that bistability arises when either the phase response curve of the neuron or the short-term depression profile changes steeply enough. The results apply to any Type I oscillator and we illustrate our findings using the Quadratic Integrate-and-Fire and Morris–Lecar neuron models.
AB - We consider a recurrent network of two oscillatory neurons that are coupled with inhibitory synapses. We use the phase response curves of the neurons and the properties of short-term synaptic depression to define Poincaré maps for the activity of the network. The fixed points of these maps correspond to phase-locked modes of the network. Using these maps, we analyze the conditions that allow short-term synaptic depression to lead to the existence of bistable phase-locked, periodic solutions. We show that bistability arises when either the phase response curve of the neuron or the short-term depression profile changes steeply enough. The results apply to any Type I oscillator and we illustrate our findings using the Quadratic Integrate-and-Fire and Morris–Lecar neuron models.
KW - Bistability
KW - Coupled oscillators
KW - Phase response curve
KW - Short-term synaptic depression
KW - Two-dimensional Poincarè map
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U2 - 10.1016/j.physd.2017.09.007
DO - 10.1016/j.physd.2017.09.007
M3 - Article
AN - SCOPUS:85032970971
SN - 0167-2789
VL - 364
SP - 8
EP - 21
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
ER -