Integrators

Monitors

# Noise¶

A collection of noise related classes and functions.

Specific noises inherit from the abstract class Noise, with each instance having its own RandomStream attribute – which is itself a Traited wrapper of Numpy’s RandomState.

tvb.simulator.noise.RandomStream[source]

This class provides the ability to create multiple random streams which can be independently seeded or set to an explicit state.

traits on this class:

init_seed (A random seed)
A random seed used to initialise the state of an instance of numpy’s RandomState.
default: 42
tvb.simulator.noise.Noise[source]

Defines a base class for noise. Specific noises are derived from this class for use in stochastic integrations.

 [KloedenPlaten_1995] Kloeden and Platen, Springer 1995, Numerical solution of stochastic differential equations.
 [ManellaPalleschi_1989] Manella, R. and Palleschi V., Fast and precise algorithm for computer simulation of stochastic differential equations, Physical Review A, Vol. 40, Number 6, 1989. [3381-3385]
 [Mannella_2002] Mannella, R., Integration of Stochastic Differential Equations on a Computer, Int J. of Modern Physics C 13(9): 1177–1194, 2002.
 [FoxVemuri_1988] Fox, R., Gatland, I., Rot, R. and Vemuri, G., * Fast , accurate algorithm for simulation of exponentially correlated colored noise*, Physical Review A, Vol. 38, Number 11, 1988. [5938-5940]
Noise.__init__()

x.__init__(...) initializes x; see help(type(x)) for signature

Noise.configure_white(dt, shape=None)[source]

Set the time step (dt) of noise or integration time

Noise.generate(shape, lo=-1.0, hi=1.0)[source]

Generate noise realization.

Noise.white(shape)[source]

Generate white noise.

Noise.coloured(shape)[source]

Generate colored noise. [FoxVemuri_1988]

traits on this class:

ntau ($$\tau$$)
The noise correlation time
default: 0.0
range: low = 0.0 ; high = 20.0
random_stream (Random Stream)
An instance of numpy’s RandomState associated with this specific Noise object.
default: None

Additive noise which, assuming the source noise is Gaussian with unit variance, will result in noise with a standard deviation of nsig.

traits on this class:

nsig ($$D$$)
The noise dispersion, it is the standard deviation of the distribution from which the Gaussian random variates are drawn. NOTE: Sensible values are typically ~<< 1% of the dynamic range of a Model’s state variables.
default: [ 1.]
range: low = 0.0 ; high = 10.0
ntau ($$\tau$$)
The noise correlation time
default: 0.0
range: low = 0.0 ; high = 20.0
random_stream (Random Stream)
An instance of numpy’s RandomState associated with this specific Noise object.
default: None
tvb.simulator.noise.Multiplicative[source]

With “external” fluctuations the intensity of the noise often depends on the state of the system. This results in the (general) stochastic differential formulation:

$dX_t = a(X_t)\,dt + b(X_t)\,dW_t$

for appropriate coefficients $$a(x)$$ and $$b(x)$$, which might be constants.

From [KloedenPlaten_1995], Equation 1.9, page 104.

traits on this class:

b ($$b$$)
A function evaluated on the state-variables, the result of which enters as the diffusion coefficient.
default: Linear(bound=False, value=None)
nsig ($$D$$)
The noise dispersion, it is the standard deviation of the distribution from which the Gaussian random variates are drawn. NOTE: Sensible values are typically ~<< 1% of the dynamic range of a Model’s state variables.
default: [ 1.]
range: low = 0.0 ; high = 10.0
ntau ($$\tau$$)
The noise correlation time
default: 0.0
range: low = 0.0 ; high = 20.0
random_stream (Random Stream)
An instance of numpy’s RandomState associated with this specific Noise object.
default: None