Neuronal Dynamics: Computational Neuroscience of Single Neurons Week 1 and Week 4: Nonlinear Integrate-and-fire Model Wulfram Gerstner EPFL, Lausanne, Switzerland Nonlinear Integrate-and-fire (NLIF) - Definition - quadratic and expon. IF - Extracting NLIF model from data - exponential Integrate-and-fire - Extracting NLIF from detailed model - from two to one dimension - Quality of NLIF? Nonlinear Integrate-and-Fire Model
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Neuronal Dynamics: Computational Neuroscience
of Single Neurons
Week 1 and Week 4:
Nonlinear Integrate-and-fire Model
Wulfram Gerstner
EPFL, Lausanne, Switzerland
Nonlinear Integrate-and-fire (NLIF) - Definition
- quadratic and expon. IF
- Extracting NLIF model from data
- exponential Integrate-and-fire
- Extracting NLIF from detailed model - from two to one dimension
- Quality of NLIF?
Nonlinear Integrate-and-Fire Model
Neuronal Dynamics – Review: Nonlinear Integrate-and Fire
)()( tRIuFudt
d
)()( tRIuuudt
drest
LIF (Leaky integrate-and-fire)
NLIF (nonlinear integrate-and-fire)
resetuu
If firing:
Neuronal Dynamics – 1.4. Leaky Integrate-and Fire revisited
LIF
ru u
If firing:
I=0 u
dt
d
u
I>0 u
dt
d
u
resting
t
u repetitive
t
)()( tRIuuudt
drest
Neuronal Dynamics – 1.4. Nonlinear Integrate-and Fire
)()( tRIuFudt
d
NLIF
ru u
firing:
I=0
u r
udt
dI>0 u
dt
d
u
Nonlinear
Integrate-and-Fire
rif u(t) = then
r
Nonlinear Integrate-and-fire Model
iui
r
)()( tRIuFudt
d
Fire+reset
NONlinear
threshold
Spike emission
reset I
j
F
rif u(t) = then
Nonlinear Integrate-and-fire Model
)()( tRIuFudt
d
Fire+reset
NONlinear
threshold
I=0 u
dt
d
u
r
I>0 u
dt
d
u
r
Quadratic I&F:
02
12 )()( ccucuF
rif u(t) = then
Nonlinear Integrate-and-fire Model
)()( tRIuFudt
d
Fire+reset
I=0 u
dt
d
u
r
I>0 u
dt
d
u
r
Quadratic I&F:
)exp()()( 0 ucuuuF rest
exponential I&F:
02
12 )()( ccucuF
rif u(t) = then
Neuronal Dynamics: Computational Neuroscience
of Single Neurons
Week 1 and Week 4:
Nonlinear Integrate-and-fire Model
Wulfram Gerstner
EPFL, Lausanne, Switzerland
Nonlinear Integrate-and-fire (NLIF) - Definition
- quadratic and expon. IF
- Extracting NLIF model from data
- exponential Integrate-and-fire
- Extracting NLIF from detailed model - from two to one dimension