Note
Click here to download the full example code
Chua's circuit
The voltage across the first capacitor of Chua's circuit spirals around one of two outer equilibria, then jumps to the other at irregular times: the double-scroll chaotic attractor.
The model is created by name from the catalog with the piecewise-linear diode and its default parameters, and runs
for 100 time units. The default blueprint shows the two capacitor voltages x and y and the inductor current z in
one time series view.
import matplotlib.pyplot as plt
from skcomplex.analysis import LyapunovAnalysis
from skcomplex.engine.runtime import Simulation
from skcomplex.engine.viz import RerunObserver
from skcomplex.models import create
MODEL = 'chua'
system = create(MODEL)
observer = RerunObserver(MODEL, save_path=f'{MODEL}.rrd', blueprint='default', interval=8)
simulation = Simulation(system, dt=0.05, observers=[observer]).check().prepare().run(until=100)
Open the recording in the Rerun viewer
The double scroll
Projected on the two capacitor voltages, the trajectory should wind around both outer equilibria in two scrolls, and the largest Lyapunov exponent of the flow should be positive.
trajectory = simulation.trajectory_
settled = trajectory.times > 10
exponents = LyapunovAnalysis(n_exponents=1, until=300.0, dt=0.01).check().prepare(system).run().exponents_
fig, ax = plt.subplots(figsize=(6, 5))
ax.plot(trajectory.values('circuit.x')[settled], trajectory.values('circuit.z')[settled], linewidth=0.5)
ax.set_xlabel('voltage x')
ax.set_ylabel('current z')
ax.set_title(f'Double scroll, largest Lyapunov exponent {exponents[0]:.2f}')
plt.show()
About the model
Chua's circuit, whose double-scroll or multiscroll attractor is chaotic.
References
- Chua, Komuro, and Matsumoto 1986
- Tang et al. 2001
- Trzaska 2023
Total running time of the script: ( 0 minutes 5.116 seconds)
Download Python source code: plot_chua.py