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
[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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