Chua Arctan

The smooth arctangent Chua variant registered by the library.

The second Chua model retained by this library is the smooth arctangent variant. It is distinct from the validated non-smooth Danca case and is not a cubic-polynomial model.

Equations

\begin{aligned} {}^C D_t^q x &= \alpha (y-x-f_s(x)),\\ {}^C D_t^q y &= x-y+z,\\ {}^C D_t^q z &= -\beta y-\gamma z,\\ f_s(x) &= a_1x+a_2\arctan(\rho x). \end{aligned}

Parameters

Parameter	Symbol	Default value
`alpha`	$\alpha$	8.4562
`beta`	$\beta$	12.0732
`gamma`	$\gamma$	0.0052
`a1`	$a_1$	0.4
`a2`	$a_2$	-1.5585
`rho`	$\rho$	1.0

import numpy as np
from hidden_attractors.models import chua_arctan_parameters, rhs_chua

params = chua_arctan_parameters()
dx = rhs_chua(np.array([0.1, 0.0, 0.0]), params)

Validation State

Validation level	Current status
Algebraic cross-tool package	pending
Integrator convergence and independent comparison	pending
Dynamic diagnostics	pending
Hiddenness basin tests	pending

The completed algebra package presently applies only to Chua Non-Smooth. The arctangent variant requires its own promoted evidence before numerical or hiddenness conclusions are published.