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The Sprott H system

Christophe LETELLIER
13/10/2009

In his research for simple quadratic chaotic systems, Julian Clinton Sprott collected more than 20 systems [1]. Most of them produce Rössler-like chaotic attractors [2]. We choose — quite arbitrarily — to include the Sprott H system that is rewritten in the form


  \left\{
    \begin{array}{l}
       \displaystyle \dot{x} =-y+z^2 \\[0.3cm]
       \displaystyle \dot{y} = x+ay \\[0.3cm]
       \displaystyle \dot{z} = x-bz
    \end{array}
  \right.

where a=0.5 and b=1. This system produces a chaotic attractor that is topologically equivalent to the Rössler attractor (Fig. 1).

JPG - 54.5 ko
Fig. 1 : Chaotic attractor solution to the Sprott H system.
Zip - 329.3 ko
Data set produced by the Sprott H system.

The data here provided corresponds to a numerical simulation of the Sprott H system with a time step \delta t=0.1 s. There are three columns that are associated with the time evolution of x, y and z, respectively.

The observability coefficients for the Sprott H system are \eta_x^2 = 0,81, \eta_y^2 = 0,88, \eta_z^2 = 1,0, that is, variables can be ranked as

 z \triangleright y \triangleright x
according to the observability they provide for the attractor.

[1] J. C. Sprott, Some simple chaotic flows, Physical Review E, 50 (2), 647-650, 1994.

[2] J.-M. Ginoux & C. Letellier, Flow curvature manifolds for shaping chaotic attractors : I Rössler-like systems, Journal of Physics A, 42, 285101, 2009.

Documents

Data set produced by the Sprott H system.
Zip · 329.3 ko
2349 - 11/12/18

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