In [1]:
%pylab nbagg
from tvb.simulator.lab import *
Populating the interactive namespace from numpy and matplotlib
   INFO  NumExpr defaulting to 4 threads.
WARNING  Field seems mutable and has a default value. Consider using a lambda as a value factory 
   attribute tvb.simulator.models.epileptor.Epileptor.state_variable_range = Final(field_type=<class 'dict'>, default={'x1': array([-2.,  1.]), 'y1': array([-20.,   2.]), 'z': array([2., 5.]), 'x2': array([-2.,  0.]), 'y2': array([0., 2.]), 'g': array([-1.,  1.])}, required=True)
WARNING  default contains values out of the declared domain. Ex 1.0 
   attribute  tvb.simulator.models.epileptor.Epileptor2D.tt = NArray(label='tt', dtype=float64, default=array([1.]), dim_names=(), ndim=None, required=True)
WARNING  Field seems mutable and has a default value. Consider using a lambda as a value factory 
   attribute tvb.simulator.models.epileptor.Epileptor2D.state_variable_range = Final(field_type=<class 'dict'>, default={'x1': array([-2.,  1.]), 'z': array([2., 5.])}, required=True)
WARNING  default contains values out of the declared domain. Ex 1.0 
   attribute  tvb.simulator.models.epileptor_rs.EpileptorRestingState.gamma_rs = NArray(label=":math:'\\gamma_rs'", dtype=float64, default=array([1.]), dim_names=(), ndim=None, required=True)
WARNING  Field seems mutable and has a default value. Consider using a lambda as a value factory 
   attribute tvb.simulator.models.epileptor_rs.EpileptorRestingState.state_variable_range = Final(field_type=<class 'dict'>, default={'x1': array([-1.8, -1.4]), 'y1': array([-15, -10]), 'z': array([3.6, 4. ]), 'x2': array([-1.1, -0.9]), 'y2': array([0.001, 0.01 ]), 'g': array([-1.,  1.]), 'x_rs': array([-2.,  4.]), 'y_rs': array([-6.,  6.])}, required=True)
WARNING  Field seems mutable and has a default value. Consider using a lambda as a value factory 
   attribute tvb.simulator.models.epileptorcodim3.EpileptorCodim3.state_variable_range = Final(field_type=<class 'dict'>, default={'x': array([0.4, 0.6]), 'y': array([-0.1,  0.1]), 'z': array([0.  , 0.15])}, required=True)
WARNING  Field seems mutable and has a default value. Consider using a lambda as a value factory 
   attribute tvb.simulator.models.epileptorcodim3.EpileptorCodim3SlowMod.state_variable_range = Final(field_type=<class 'dict'>, default={'x': array([0.4, 0.6]), 'y': array([-0.1,  0.1]), 'z': array([0. , 0.1]), 'uA': array([0., 0.]), 'uB': array([0., 0.])}, required=True)
WARNING  Field seems mutable and has a default value. Consider using a lambda as a value factory 
   attribute tvb.simulator.models.hopfield.Hopfield.state_variable_range = Final(field_type=<class 'dict'>, default={'x': array([-1.,  2.]), 'theta': array([0., 1.])}, required=True)
WARNING  default contains values out of the declared domain. Ex 0.12 
   attribute  tvb.simulator.models.jansen_rit.JansenRit.p_min = NArray(label=':math:`p_{min}`', dtype=float64, default=array([0.12]), dim_names=(), ndim=None, required=True)
WARNING  default contains values out of the declared domain. Ex 0.32 
   attribute  tvb.simulator.models.jansen_rit.JansenRit.p_max = NArray(label=':math:`p_{max}`', dtype=float64, default=array([0.32]), dim_names=(), ndim=None, required=True)
WARNING  default contains values out of the declared domain. Ex 0.22 
   attribute  tvb.simulator.models.jansen_rit.JansenRit.mu = NArray(label=':math:`\\mu_{max}`', dtype=float64, default=array([0.22]), dim_names=(), ndim=None, required=True)
WARNING  Field seems mutable and has a default value. Consider using a lambda as a value factory 
   attribute tvb.simulator.models.jansen_rit.JansenRit.state_variable_range = Final(field_type=<class 'dict'>, default={'y0': array([-1.,  1.]), 'y1': array([-500.,  500.]), 'y2': array([-50.,  50.]), 'y3': array([-6.,  6.]), 'y4': array([-20.,  20.]), 'y5': array([-500.,  500.])}, required=True)
WARNING  Field seems mutable and has a default value. Consider using a lambda as a value factory 
   attribute tvb.simulator.models.jansen_rit.ZetterbergJansen.state_variable_range = Final(field_type=<class 'dict'>, default={'v1': array([-100.,  100.]), 'y1': array([-500.,  500.]), 'v2': array([-100.,   50.]), 'y2': array([-100.,    6.]), 'v3': array([-100.,    6.]), 'y3': array([-100.,    6.]), 'v4': array([-100.,   20.]), 'y4': array([-100.,   20.]), 'v5': array([-100.,   20.]), 'y5': array([-500.,  500.]), 'v6': array([-100.,   20.]), 'v7': array([-100.,   20.])}, required=True)
WARNING  default contains values out of the declared domain. Ex -0.01 
   attribute  tvb.simulator.models.larter_breakspear.LarterBreakspear.TCa = NArray(label=':math:`T_{Ca}`', dtype=float64, default=array([-0.01]), dim_names=(), ndim=None, required=True)
WARNING  default contains values out of the declared domain. Ex 0.3 
   attribute  tvb.simulator.models.larter_breakspear.LarterBreakspear.TNa = NArray(label=':math:`T_{Na}`', dtype=float64, default=array([0.3]), dim_names=(), ndim=None, required=True)
WARNING  default contains values out of the declared domain. Ex 2.0 
   attribute  tvb.simulator.models.larter_breakspear.LarterBreakspear.aei = NArray(label=':math:`a_{ei}`', dtype=float64, default=array([2.]), dim_names=(), ndim=None, required=True)
WARNING  default contains values out of the declared domain. Ex 2.0 
   attribute  tvb.simulator.models.larter_breakspear.LarterBreakspear.aie = NArray(label=':math:`a_{ie}`', dtype=float64, default=array([2.]), dim_names=(), ndim=None, required=True)
WARNING  default contains values out of the declared domain. Ex 1.0 
   attribute  tvb.simulator.models.larter_breakspear.LarterBreakspear.ane = NArray(label=':math:`a_{ne}`', dtype=float64, default=array([1.]), dim_names=(), ndim=None, required=True)
WARNING  default contains values out of the declared domain. Ex 0.3 
   attribute  tvb.simulator.models.larter_breakspear.LarterBreakspear.Iext = NArray(label=':math:`I_{ext}`', dtype=float64, default=array([0.3]), dim_names=(), ndim=None, required=True)
WARNING  default contains values out of the declared domain. Ex 1.0 
   attribute  tvb.simulator.models.larter_breakspear.LarterBreakspear.QV_max = NArray(label=':math:`Q_{max}`', dtype=float64, default=array([1.]), dim_names=(), ndim=None, required=True)
WARNING  default contains values out of the declared domain. Ex 1.0 
   attribute  tvb.simulator.models.larter_breakspear.LarterBreakspear.QZ_max = NArray(label=':math:`Q_{max}`', dtype=float64, default=array([1.]), dim_names=(), ndim=None, required=True)
WARNING  default contains values out of the declared domain. Ex 1.0 
   attribute  tvb.simulator.models.larter_breakspear.LarterBreakspear.t_scale = NArray(label=':math:`t_{scale}`', dtype=float64, default=array([1.]), dim_names=(), ndim=None, required=True)
WARNING  Field seems mutable and has a default value. Consider using a lambda as a value factory 
   attribute tvb.simulator.models.larter_breakspear.LarterBreakspear.state_variable_range = Final(field_type=<class 'dict'>, default={'V': array([-1.5,  1.5]), 'W': array([-1.5,  1.5]), 'Z': array([-1.5,  1.5])}, required=True)
WARNING  Field seems mutable and has a default value. Consider using a lambda as a value factory 
   attribute tvb.simulator.models.linear.Linear.state_variable_range = Final(field_type=<class 'dict'>, default={'x': array([-1,  1])}, required=True)
WARNING  default contains values out of the declared domain. Ex 1.0 
   attribute  tvb.simulator.models.oscillator.Generic2dOscillator.gamma = NArray(label=':math:`\\gamma`', dtype=float64, default=array([1.]), dim_names=(), ndim=None, required=True)
WARNING  Field seems mutable and has a default value. Consider using a lambda as a value factory 
   attribute tvb.simulator.models.oscillator.Generic2dOscillator.state_variable_range = Final(field_type=<class 'dict'>, default={'V': array([-2.,  4.]), 'W': array([-6.,  6.])}, required=True)
WARNING  Field seems mutable and has a default value. Consider using a lambda as a value factory 
   attribute tvb.simulator.models.oscillator.Kuramoto.state_variable_range = Final(field_type=<class 'dict'>, default={'theta': array([0.        , 6.28318531])}, required=True)
WARNING  Field seems mutable and has a default value. Consider using a lambda as a value factory 
   attribute tvb.simulator.models.oscillator.SupHopf.state_variable_range = Final(field_type=<class 'dict'>, default={'x': array([-5.,  5.]), 'y': array([-5.,  5.])}, required=True)
WARNING  Field seems mutable and has a default value. Consider using a lambda as a value factory 
   attribute tvb.simulator.models.stefanescu_jirsa.ReducedSetFitzHughNagumo.state_variable_range = Final(field_type=<class 'dict'>, default={'xi': array([-4.,  4.]), 'eta': array([-3.,  3.]), 'alpha': array([-4.,  4.]), 'beta': array([-3.,  3.])}, required=True)
WARNING  default contains values out of the declared domain. Ex 1.0 
   attribute  tvb.simulator.models.stefanescu_jirsa.ReducedSetHindmarshRose.a = NArray(label=':math:`a`', dtype=float64, default=array([1.]), dim_names=(), ndim=None, required=True)
WARNING  default contains values out of the declared domain. Ex 3.0 
   attribute  tvb.simulator.models.stefanescu_jirsa.ReducedSetHindmarshRose.b = NArray(label=':math:`b`', dtype=float64, default=array([3.]), dim_names=(), ndim=None, required=True)
WARNING  default contains values out of the declared domain. Ex 1.0 
   attribute  tvb.simulator.models.stefanescu_jirsa.ReducedSetHindmarshRose.c = NArray(label=':math:`c`', dtype=float64, default=array([1.]), dim_names=(), ndim=None, required=True)
WARNING  default contains values out of the declared domain. Ex 3.3 
   attribute  tvb.simulator.models.stefanescu_jirsa.ReducedSetHindmarshRose.mu = NArray(label=':math:`\\mu`', dtype=float64, default=array([3.3]), dim_names=(), ndim=None, required=True)
WARNING  Field seems mutable and has a default value. Consider using a lambda as a value factory 
   attribute tvb.simulator.models.stefanescu_jirsa.ReducedSetHindmarshRose.state_variable_range = Final(field_type=<class 'dict'>, default={'xi': array([-4.,  4.]), 'eta': array([-25.,  20.]), 'tau': array([ 2., 10.]), 'alpha': array([-4.,  4.]), 'beta': array([-20.,  20.]), 'gamma': array([ 2., 10.])}, required=True)
WARNING  Field seems mutable and has a default value. Consider using a lambda as a value factory 
   attribute tvb.simulator.models.wilson_cowan.WilsonCowan.state_variable_range = Final(field_type=<class 'dict'>, default={'E': array([0., 1.]), 'I': array([0., 1.])}, required=True)
WARNING  default contains values out of the declared domain. Ex 0.27 
   attribute  tvb.simulator.models.wong_wang.ReducedWongWang.a = NArray(label=':math:`a`', dtype=float64, default=array([0.27]), dim_names=(), ndim=None, required=True)
WARNING  Field seems mutable and has a default value. Consider using a lambda as a value factory 
   attribute tvb.simulator.models.wong_wang.ReducedWongWang.state_variable_range = Final(field_type=<class 'dict'>, default={'S': array([0., 1.])}, required=True)
WARNING  Field seems mutable and has a default value. Consider using a lambda as a value factory 
   attribute tvb.simulator.models.wong_wang.ReducedWongWang.state_variable_boundaries = Final(field_type=<class 'dict'>, default={'S': array([0., 1.])}, required=True)
WARNING  default contains values out of the declared domain. Ex 10.0 
   attribute  tvb.simulator.models.wong_wang_exc_inh.ReducedWongWangExcInh.tau_i = NArray(label=':math:`\\tau_i`', dtype=float64, default=array([10.]), dim_names=(), ndim=None, required=True)
WARNING  Field seems mutable and has a default value. Consider using a lambda as a value factory 
   attribute tvb.simulator.models.wong_wang_exc_inh.ReducedWongWangExcInh.state_variable_range = Final(field_type=<class 'dict'>, default={'S_e': array([0., 1.]), 'S_i': array([0., 1.])}, required=True)
WARNING  Field seems mutable and has a default value. Consider using a lambda as a value factory 
   attribute tvb.simulator.models.wong_wang_exc_inh.ReducedWongWangExcInh.state_variable_boundaries = Final(field_type=<class 'dict'>, default={'S_e': array([0., 1.]), 'S_i': array([0., 1.])}, required=True)
WARNING  Field seems mutable and has a default value. Consider using a lambda as a value factory 
   attribute tvb.simulator.models.zerlaut.ZerlautFirstOrder.state_variable_range = Final(field_type=<class 'dict'>, default={'E': array([0. , 0.1]), 'I': array([0. , 0.1]), 'W': array([  0., 100.])}, required=True)
WARNING  Field seems mutable and has a default value. Consider using a lambda as a value factory 
   attribute tvb.simulator.models.zerlaut.ZerlautSecondOrder.state_variable_range = Final(field_type=<class 'dict'>, default={'E': array([0. , 0.1]), 'I': array([0. , 0.1]), 'C_ee': array([0., 0.]), 'C_ei': array([0., 0.]), 'C_ii': array([0., 0.]), 'W': array([  0., 100.])}, required=True)
WARNING  Field seems mutable and has a default value. Consider using a lambda as a value factory 
   attribute tvb.datatypes.time_series.TimeSeries.labels_dimensions = Attr(field_type=<class 'dict'>, default={}, required=True)
WARNING  Field seems mutable and has a default value. Consider using a lambda as a value factory 
   attribute tvb.datatypes.projections.ProjectionMatrix.conductances = Attr(field_type=<class 'dict'>, default={'air': 0.0, 'skin': 1.0, 'skull': 0.01, 'brain': 1.0}, required=False)
WARNING  default contains values out of the declared domain. Ex 1.0 
   attribute  tvb.simulator.coupling.HyperbolicTangent.b = NArray(label=':math:`b`', dtype=float64, default=array([1.]), dim_names=(), ndim=None, required=True)
WARNING  default contains values out of the declared domain. Ex 1.0 
   attribute  tvb.simulator.coupling.Kuramoto.a = NArray(label=':math:`a`', dtype=float64, default=array([1.]), dim_names=(), ndim=None, required=True)

Simulate with the Jansen and Rit model.

White noise is added to one specific state variable to emulate the external stochastic stimulus p(t) as described in [JansenRit_1995]

In [2]:
jrm = models.JansenRit(mu=numpy.array([0.]), v0=numpy.array([6.]))

phi_n_scaling = (jrm.a * jrm.A * (jrm.p_max-jrm.p_min) * 0.5 )**2 / 2.
sigma         = numpy.zeros(6) 
sigma[3]      = phi_n_scaling

# the other aspects of the simulator are standard
sim = simulator.Simulator(
    model=jrm,
    connectivity=connectivity.Connectivity.from_file(),
    coupling=coupling.SigmoidalJansenRit(a=numpy.array([10.0])),
    integrator=integrators.HeunStochastic(dt=2 ** -4, noise=noise.Additive(nsig=sigma)),
    monitors=(monitors.TemporalAverage(period=2 ** -2),),
    simulation_length=1e3,
).configure()

# run it
(time, data), = sim.run()

# visualize time series
figure()
plot(time, data[:, 0, :, 0], 'k', alpha=0.1)
title("Temporal Average")
WARNING  File 'hemispheres' not found in ZIP.
/root/tvb-root/scientific_library/tvb/simulator/coupling.py:365: RuntimeWarning: overflow encountered in exp
  pre = self.cmax / (1.0 + numpy.exp(self.r * (self.midpoint - (x_j[:, 0] - x_j[:, 1]))))
/root/tvb-root/scientific_library/tvb/simulator/models/jansen_rit.py:273: RuntimeWarning: overflow encountered in _numba_dfun_jr
  self.A, self.b, self.B, self.J, self.mu
Out[2]:
Text(0.5, 1.0, 'Temporal Average')