The Rucklidge system

Christophe LETELLIER

23/05/2009

The Rucklidge system [1]

$\left\{ \begin{array}{l} \dot{x} = y \\[0.1cm] \dot{y} = -\lambda x + \kappa y -xz \\[0.1cm] \dot{z} = -z + x^2 \end{array} \right.$
is a Lorenz-like system but with quite specific observability features. The behavior proposed for this challenge corresponds to parameters $\lambda=-6.7$ and $\kappa=-2$ .


Fig. 1 : Chaotic "Lorenz" attractor solution to the Rucklidge system.


Data set for the Rucklidge dynamics.

A 100,000 data-points time series with the three variables is available here.

The observability coefficients for the Rucklidge system are $\eta_x^2 = 0.88$ , $\eta_y^2 = 0.27$ , $\eta_z^2 = 0.44$ , that is, the dynamical variables can be ranked as

$x \triangleright z \triangleright y$ .

[1] A. M. Rucklidge, Chaos in models of double convection, Journal of Fluid Mechanics, 237, 209-229, 1992.

Documents

Data set for the Rucklidge dynamics.

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25404 - 13/10/24

| MàJ . 04/02/2024