nsim.models package

Submodules

nsim.models.basic_sde module

Simple Stochastic Differential Equation models

classes:
OU 1D Ornstein Uhlenbeck model
class nsim.models.basic_sde.OU

Bases: nsim.nsim.SDEModel

G(y, t)
dimension = 1
f(y, t)
lam = -1.0
output_vars = [0]
sigma = 0.8
y0 = array([ 0.])

nsim.models.neural_mass module

Large scale population models for neuroscience.

classes:
JansenRit
class nsim.models.neural_mass.JansenRit

Bases: nsim.nsim.SDEModel

Jansen-Rit neural mass model of a small cortical region.

By default, it simulates the model of Jansen and Rit (1995)

It also implements the extended equations given by Aburn et al. (2012) allowing input to both pyramidal cells and spiny stellate cells. (If you set u_mean and u_sdev to nonzero values)

See also

Jansen, B. Rit, V. (1995) Electroencephalogram and visual evoked potential generation in a mathematical model of coupled cortical columns

Aburn et al. (2012) Critical fluctuations in cortical models near instability

G(v, t)

Aburn2012 equations right hand side, noise term :param v: (8,) array

state vector
Parameters:t – number scalar time
Returns:(8,8) array Only one matrix column is non-zero, meaning that in this example we are modelling the noise input to pyramidal and spiny populations as fully correlated. To simulate uncorrelated inputs instead, change [5,0] to [5,1].
He1 = 3.25
He2 = 3.25
He3 = 3.25
Hi = 22.0
S(y)
average_timestep_used_by_jr = 0.0012
dimension = 8
e0 = 2.5
f(v, t)

Aburn2012 equations right hand side, noise free term :param v: (8,) array

state vector
Parameters:t – number scalar time
Returns:(8,) array
g1 = 675.0
g2 = 540.0
g3 = 168.75
g4 = 168.75
ke1 = 100.0
ke2 = 100.0
ke3 = 100.0
ki = 50.0
output_vars = [1, 2]
p_mean = 220.0
p_sdev = 2.0
rho1 = 0.56
rho2 = 6.0
u_mean = 0.0
u_sdev = 0.0
y0 = array([ 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.])

nsim.models.oscillators module

Simple oscillator models

classes:
Oscillator
class nsim.models.oscillators.Oscillator

Bases: nsim.nsim.SDEModel

G(y, t)
dimension = 2
f(y, t)
lam = -10.0
omega = 125.66370614359172
output_vars = [0]
sigma1 = 0.01
sigma2 = 0.01
y0 = array([ 1., 1.])
class nsim.models.oscillators.Oscillator1D

Bases: nsim.nsim.SDEModel

G(y, t)
epsilon = 0.6
f(y, t)
sigma = 0.03
y0 = array([ 0.])

Module contents

class nsim.models.JansenRit

Bases: nsim.nsim.SDEModel

Jansen-Rit neural mass model of a small cortical region.

By default, it simulates the model of Jansen and Rit (1995)

It also implements the extended equations given by Aburn et al. (2012) allowing input to both pyramidal cells and spiny stellate cells. (If you set u_mean and u_sdev to nonzero values)

See also

Jansen, B. Rit, V. (1995) Electroencephalogram and visual evoked potential generation in a mathematical model of coupled cortical columns

Aburn et al. (2012) Critical fluctuations in cortical models near instability

G(v, t)

Aburn2012 equations right hand side, noise term :param v: (8,) array

state vector
Parameters:t – number scalar time
Returns:(8,8) array Only one matrix column is non-zero, meaning that in this example we are modelling the noise input to pyramidal and spiny populations as fully correlated. To simulate uncorrelated inputs instead, change [5,0] to [5,1].
He1 = 3.25
He2 = 3.25
He3 = 3.25
Hi = 22.0
S(y)
average_timestep_used_by_jr = 0.0012
dimension = 8
e0 = 2.5
f(v, t)

Aburn2012 equations right hand side, noise free term :param v: (8,) array

state vector
Parameters:t – number scalar time
Returns:(8,) array
g1 = 675.0
g2 = 540.0
g3 = 168.75
g4 = 168.75
ke1 = 100.0
ke2 = 100.0
ke3 = 100.0
ki = 50.0
output_vars = [1, 2]
p_mean = 220.0
p_sdev = 2.0
rho1 = 0.56
rho2 = 6.0
u_mean = 0.0
u_sdev = 0.0
y0 = array([ 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.])
class nsim.models.OU

Bases: nsim.nsim.SDEModel

G(y, t)
dimension = 1
f(y, t)
lam = -1.0
output_vars = [0]
sigma = 0.8
y0 = array([ 0.])
class nsim.models.Oscillator

Bases: nsim.nsim.SDEModel

G(y, t)
dimension = 2
f(y, t)
lam = -10.0
omega = 125.66370614359172
output_vars = [0]
sigma1 = 0.01
sigma2 = 0.01
y0 = array([ 1., 1.])
class nsim.models.Oscillator1D

Bases: nsim.nsim.SDEModel

G(y, t)
epsilon = 0.6
f(y, t)
sigma = 0.03
y0 = array([ 0.])