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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.

PNG - 72.6 ko
Fig. 1 : Chaotic "Lorenz" attractor solution to the Rucklidge system.
Zip - 1.3 Mo
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.
Zip · 1.3 Mo
2173 - 20/10/18

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