dynamo.vf.gen_fixed_points

dynamo.vf.gen_fixed_points(func, auto_func, dim_range, RandNum, EqNum, reverse=False, grid_num=50, x_ini=None)[source]

Calculate the fixed points of (learned) vector field function . Classify the fixed points into classes of stable and saddle points based on the eigenvalue of the Jacobian on the point.

Parameters

  • func ('function') – The function of the (learned) vector field function that are required to fixed points for

  • auto_func ('np.ndarray' (not used)) – The function that is written with autograd of the same ODE equations that is used to calculate the Jacobian matrix. If auto_func is set to be None, Jacobian is calculated through the fjac, r returned from fsolve.

  • dim_range ('list') – The range of variables in the ODE equations

  • RandNum ('int') – The number of random initial points to sample

  • EqNum ('int') – The number of equations (dimension) of the system

  • reverse (bool) – Whether to reverse the sign (direction) of vector field (VF).

  • grid_num (int (default: 50)) – The number of grids on each dimension, only used when the EqNum is 2 and x_ini is None.

  • x_ini ('np.ndarray') – The user provided initial points that is used to find the fixed points

Returns

  • stable (‘np.ndarray’) – A matrix consists of the coordinates of the stable steady state

  • saddle (‘np.ndarray’) – A matrix consists of the coordinates of the unstable steady state