hundun

hundun is a python library for the exploration of chaos.
Please note that this library is in beta phase.

Example

Import the package's equation object.

from hundun import Differential

Crating a differential equation is easy using Differential. The important thing is to define parameter() and equation() as methods.

class Lorenz(Differential):

    def parameter(self, s=10, r=28, b=8/3):
        self.s, self.r, self.b = s, r, b
        self.dim = 3

    def equation(self, t, u):
        s, r, b = self.s, self.r, self.b

        x, y, z = u

        x_dot = s*(y - x)
        y_dot = r*x - y - x*z
        z_dot = x*y - b*z

        return x_dot, y_dot, z_dot

Various methods can be used by creating an instance of Lorenz. As a test, use .solve_n_times to solve the equation in 5000 steps. (This method uses RK4 by default.)

l = Lorenz.on_attractor()
l.solve_n_times(5000)

At this time, you can get the time and orbit by using .t_seq and .u_seq.

It is possible to calculate the Lyapunov exponent(spectrum) from the orbit using Lorenz above. In addition, a calculation method based on QR decomposition can be used by defining jacobian()(Jacoby matrix).

class Lorenz2(Lorenz):
    def jacobian(self):
        s, r, b = self.s, self.r, self.b
        x, y, z = self.u

        j = [[-s, s, 0],
             [r-z, -1, -x],
             [y, x, -b]]

        return j

calc_les automatically determines and calculates.

from hundun.lyapunov import calc_les

les_seq, les = calc_les(Lorenz2)

Also, you can easily draw by using Drawing of utils.

from hundun.utils import Drawing

d = Drawing(1, 2, three=1, number=True)

d[0,0].plot(l.u_seq[:,0], l.u_seq[:,1], l.u_seq[:,2])
d[0,0].set_axis_label('x', 'y', 'z')

for i in range(3):
    d[0,1].plot(les_seq[:, i], label=fr'$\lambda_{i+1}=${les[i]:>+8.3f}')
d[0,1].legend(loc='center right')
d[0,1].set_axis_label('step', r'\lambda')

d.show()

Currently, time series analysis methods are being added!

Installation

hundun can be installed via pip from PyPI.

pip install hundun

To use the latest code (unstable), checkout the dev branch and run above command in the main hundun directory.

pip install .

Dependencies

[ Numpy ] [ Scipy ] [ Matplotlib ]