class_docstr: Simulates the velocity of a dissipative soliton (kind of self organized particle) [6]_.
  The equilibrium velocity without noise R=0 for
  $   au>1.0/\kappa_3$ is $\kappa_3 \sqrt{(tau - 1.0/\kappa_3)/Q}.
  Before the drift-bifurcation $      au \le 1.0/\kappa_3$ the velocity is zero.
  
  References
  ----------
  
  .. [6] Andreas Kempa-Liehr (2013, p. 159-170)
      Dynamics of Dissipative Soliton
      Dissipative Solitons in Reaction Diffusion Systems.
      Springer: Berlin
  
  
  >>> ds = velocity(tau=3.5) # Dissipative soliton with equilibrium velocity 1.5e-3
  >>> print(ds.label) # Discriminating before or beyond Drift-Bifurcation
  1
  
  # Equilibrium velocity
  >>> print(ds.deterministic)
  0.0015191090506254991
  
  # Simulated velocity as a time series with 20000 time steps being disturbed by Gaussian white noise
  >>> v = ds.simulate(20000)
docstr: :param N: number of time steps
  :type N: int
  :param v0: initial velocity vector
  :type v0: ndarray
  :return: time series of velocity vectors with shape (N, v0.shape[0])
  :rtype: ndarray
code: def simulate(self, N, v0=np.zeros(2)):
      """
  
      :param N: number of time steps
      :type N: int
      :param v0: initial velocity vector
      :type v0: ndarray
      :return: time series of velocity vectors with shape (N, v0.shape[0])
      :rtype: ndarray
      """
  
      v = [v0]  # first value is initial condition
      n = N - 1  # Because we are returning the initial condition,
      # only (N-1) time steps are computed
      gamma = np.random.randn(n, v0.size)
      for i in range(n):
          next_v = self.__call__(v[i]) + self.c * gamma[i]
          v.append(next_v)
      v_vec = np.array(v)
      return v_vec
  
file_path: tsfresh/tsfresh/examples/driftbif_simulation.py
imports: import logging
  import numpy
  import pandas
label_desc: Use image node_id 3 for calling the velocity obj's underlying member method code with example usage: obj.simulate(N, v0) and returns: v_vec