Tsucs2¶

Systems / ODEs / Coupled systems

The Three-Scroll Unified Chaotic System (TSUCS-2), a Dequan-Li-family flow unifying several three-scroll attractors.

continuous · ODE3 dimensionschaotic

Interactive: drag to rotate

Definition¶

\[ \begin{aligned} \dot{y_{0}} &= - a y_{0} + a y_{1} + d y_{0} y_{2} \\ \dot{y_{1}} &= f y_{1} + k y_{0} - y_{0} y_{2} \\ \dot{y_{2}} &= c y_{2} - eps y_{0}^{2} + y_{0} y_{1} \end{aligned} \]

Parameters¶

Symbol	Default	Role
`a`	`40`	x–y coupling gain
`c`	`0.833`	z self-feedback
`d`	`0.5`	x·z term strength
`eps`	`0.65`	x² term strength
`f`	`20`	y self-feedback
`k`	`0`	y forcing gain

Properties¶

Lyapunov spectrum

$-0.0007164,\; +0.02415,\; -1.492$
computed at build

Kaplan–Yorke dimension

$D_{KY} = 2.016$

Divergence ∇·f

$\nabla\!\cdot f = - a + c + d y_{2} + f$
state-dependent

Equilibria

1 equilibria
0 stable · 1 unstable

Define it in TSDynamics¶

import tsdynamics as ts

sys = ts.systems.Tsucs2()
traj = sys.integrate(final_time=100.0, dt=0.01)

exps = sys.lyapunov_spectrum()
ts.kaplan_yorke_dimension(exps)

Reference¶

Pan, Zhou & Li (2013), Nonlinear Dyn. 73, 1965-1976

BibTeX

@misc{tsucs2,
  title = {Tsucs2 system},
  note = {Pan, Zhou & Li (2013), Nonlinear Dyn. 73, 1965-1976}
}