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).

**Fig. 1 : Chaotic attractor solution to the Sprott H system.**

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 (…)

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