Phase Resetting Neural Oscillators: Topological Theory Versus the RealWorld

2011 ◽  
pp. 33-51 ◽  
Author(s):  
Trine Krogh-Madsen ◽  
Robert Butera ◽  
G. Bard Ermentrout ◽  
Leon Glass
Keyword(s):  
Phase Resetting ◽  
Neural Oscillators ◽  
Topological Theory ◽  
Theory Versus

scholarly journals Phase resetting and coupling of noisy neural oscillators

2006 ◽  
Vol 20 (2) ◽  
pp. 179-190 ◽  
Author(s):  
Bard Ermentrout ◽  
David Saunders
Keyword(s):  
Phase Resetting ◽  
Neural Oscillators

scholarly journals All Phase Resetting Curves Are Bimodal, but Some Are More Bimodal Than Others

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Sorinel A. Oprisan
Keyword(s):  
Hopf Bifurcation ◽  
Oscillatory Behavior ◽  
Positive Phase ◽  
Neural Oscillator ◽  
Phase Resetting ◽  
Invariant Circle ◽  
Neural Oscillators ◽  
External Stimuli ◽  
Firing Period ◽  
Phase Resetting Curves

Phase resetting curves (PRCs) are phenomenological and quantitative tools that tabulate the transient changes in the firing period of endogenous neural oscillators as a result of external stimuli, for example, presynaptic inputs. A brief current perturbation can produce either a delay (positive phase resetting) or an advance (negative phase resetting) of the subsequent spike, depending on the timing of the stimulus. We showed that any planar neural oscillator has two remarkable points, which we called neutral points, where brief current perturbations produce no phase resetting and where the PRC flips its sign. Since there are only two neutral points, all PRCs of planar neural oscillators are bimodal. The degree of bimodality of a PRC, that is, the ratio between the amplitudes of the delay and advance lobes of a PRC, can be smoothly adjusted when the bifurcation scenario leading to stable oscillatory behavior combines a saddle node of invariant circle (SNIC) and an Andronov-Hopf bifurcation (HB).

scholarly journals Maps based on the phase resetting curve explain spike statistics of coupled neural oscillators observed in the presence of noise

2010 ◽  
Vol 11 (S1) ◽  
Author(s):  
Srisairam Achuthan ◽  
Jianxia Cui ◽  
Robert Butera ◽  
Carmen C Canavier
Keyword(s):  
Phase Resetting ◽  
Neural Oscillators
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