Dynamics of Perceptual Bistability
J Rinzel, NYU
w/ N Rubin, A Shpiro, R Curtu, R Moreno
• Alternations in perception of ambiguous stimulus – irregular…
• Oscillator models – mutual inhibition, switches due to adaptation
-- noise gives randomness to period
• Attractor models – noise driven, no alternation w/o noise
• Constraints from data: <T>, CV
Which model is favored?
Mutual inhibition with
slow adaptation 
alternating dominance
and suppression
IV:
Levelt, 1968
Oscillator Models for Directly Competing Populations
Two mutually inhibitory populations, corresponding to each percept.
Firing rate model: r1(t), r2(t)
Slow negative feedback: adaptation or synaptic depression.
f
r1r11
r2r2
f
Slow adaptation, a1(t)
u
τ dr1/dt = -r1 + f(-βr2 - g a1+ I1)
τa da1/dt = -a1 + r1
No recurrent excitation
…half-center oscillator
τ dr2/dt = -r2 + f(-βr1 - g a2+ I2)
τa da2/dt = -a2 + r2
τa >> τ ,
f(u)=1/(1+exp[(θ-u)/k])
w/ N Rubin, A Shpiro, R Curtu
Shpiro et al, J Neurophys 2007
Wilson 2003; Laing and Chow 2003
Alternating firing rates
Adaptation slowly grows/decays
WTA or ATT regime
IV
adaptation LC model
Analysis of Dynamics
Fast-Slow dissection: r1 , r2 fast variables
a1 , a2 slow variables
a1, a2 frozen
r1- nullcline
r2- nullcline
r1 = f(-βr2 - g a1+ I1)
r2 = f(-βr1 - g a2+ I2)
r2
r1
r1-r2 phase plane, slowly drifting nullclines
r1- nullcline
r2- nullcline
r2
At a switch:
• saddle-node in fast dynamics.
• dominant r is high while system rides
near “threshold” of suppressed populn’s
nullcline  ESCAPE.
Switching occurs when a1-a2
traj reaches a curve of SNs (knees)
r1
β =0.9, I1=I2=1.4
a2
a1
Switching due to adaptation:
release or escape mechanism
f
input
net input
net input
Small I, “release”
Large I, “escape”
Dominant, a ↑
I–ga
θ
I+αa–ga
θ
Suppressed, a ↓
I–ga-β
Recurrent excitation, secures “escape”
Noise leads to random dominance
durations and eliminates WTA behavior.
τ dri/dt = -ri+ f(-βrj - g ai+ Ii + ni)
τa dai/dt = -ai + ri
Added to stimulus I1,2
s.d., σ = 0.03, τn = 10
Model with synaptic depression
Noise-Driven Attractor Models
w/ R Moreno, N Rubin
J Neurophys, 2007
No oscillations if
noise is absent.
Kramers 1940
LP-IV in an attractor model
Compare dynamical skeletons: “oscillator” and attractor-based models
activity
WTA
rA=rB
OSC
gA= gB
Observed variability and mean duration constrain the model.
With noise
1 sec < mean T < 10 sec
0.4 < CV < 0.6
Noise-free
Difficult to arrange low CV and
high <T> in OSC regime.
Favored: noise-driven attractor with weak adaptation – but not
far from oscillator regime.
With noise
Best fit distribution depends on parameter values.
Noise dominated
Adaptation dominated
I1 , I2 = 0.6
SUMMARY
Swartz Foundation and NIH.
w/ N Rubin, A Shpiro, R Curtu, R Moreno
Experimentally:
• Monotonic <T> vs I
• <T> and CV as constraints
• No correlation between successive cycles
Models, one framework – vary params.
Mutual, direct inhibition; w/o recurrent excitation
Non-monotonic dominance duration vs I1, I2
• Attractor regime, noise dominated
• Better match w/ data.
• Balance between noise level and adaptation strength.
• Oscillator regime, adaptation dominated
• Relatively smaller CV.
• Relatively greater correlation between successive cycles.
• Moreno model (J Neurophys 2007): local inhibition, strong recurrent
excitation: monotonic <T> vs I.