class brainpy.dyn.OUProcess(size, mean=0.0, sigma=1.0, tau=10.0, method='exp_euler', keep_size=False, mode=None, name=None)[source]#

The Ornstein–Uhlenbeck process.

The Ornstein–Uhlenbeck process \(x_{t}\) is defined by the following stochastic differential equation:

\[\tau dx_{t}=-\theta \,x_{t}\,dt+\sigma \,dW_{t}\]

where \(\theta >0\) and \(\sigma >0\) are parameters and \(W_{t}\) denotes the Wiener process.

  • size (int, sequence of int) – The model size.

  • mean (Parameter) – The noise mean value.

  • sigma (Parameter) – The noise amplitude.

  • tau (Parameter) – The decay time constant.

  • method (str) – The numerical integration method for stochastic differential equation.

  • name (str) – The model name.

reset_state(batch_or_mode=None, **kwargs)[source]#

Reset function which resets local states in this model.

Simply speaking, this function should implement the logic of resetting of local variables in this node.

See https://brainpy.readthedocs.io/en/latest/tutorial_toolbox/state_resetting.html for details.


The function to specify the updating rule.