A NEURAL MECHANISM FOR THE EMERGENCE OF
NON-CRITICAL POWER LAWS
Serena Di Santo
21/06/2016Lake Como School
tissue on array local field potentials thresholded signals
A NEURAL MECHANISM FOR THE EMERGENCE OF
NON-CRITICAL POWER LAWS
c r i t i c a l
WILSON-COWAN MODEL AND BALANCED AMPLIFICATION OF FLUCTUATIONS
E
I
�wI
�wI
wE
wE
@tE = �↵E + (1� E)f(s)
@tI = �↵I + (1� I)f(s)
f(s) =✓[tanh(
s)]
s = wEE � wII + h
'
Benayoun M, Cowan JD, van Drongelen W, Wallace E, (2010) PLoS Comput Biol Murphy BK, Miller K, (2009) Neuron
wE wI
E
I
not balanced
+p
↵E + (1� E)f(s)⌘E
+p
↵I + (1� I)f(s)⌘I
NON NORMAL FORMS AND A NOISE INDUCED ZERO MODE
Linear stability close to the fixed point…
Non Diagonalizable
Non orthogonal Eigenvect
Define Pseudospectra
⇢ = a⇢� b⇢2 + h+ �p⇢⌘(t)
T U N NE LI N G
Amplificated fluctuations+noise
☞
NON NORMAL FORM
ATA 6= AAT
Pst(⇢) ⇠1
⇢1�2h�2
SIMILAR PHENOMENON, DIFFERENT REGULATORY MECHANISM: TSODYKS-MARKRAM MODEL FOR SYNAPTIC PLASTICITY
R =1
⌧(Rm �R)� u⇢R⇢ = a⇢� b⇢
2 � c⇢3 + !⇢R+ �
p⇢⌘⇢ = a⇢� b⇢2 � c⇢
3 + h+ !⇢R+ �p⇢⌘
NON-NORMAL FORMS☞ AMPLIFICATION OF FLUCTUATIONS ☞
NOISE INDUCED ZERO MODE☞ ☞ NON-CRITICAL POWER LAWS