Christophe LETELLIER
23/05/2009

The modified hyperchaotic Rössler system [1]

was proposed to ensure its
synchronization using a single variable. It corresponds to the original hyperchaotic
Rössler system [2] rewritten replacing *(x,y,z,w)* with *(x,y,z,v=y+w)*.
This four dimensional system produces a hyperchaotic attractor (Fig. 1).

**Fig. 1 : Hyperchaotic attractor solution to the modified hyperchaotic Rössler system.**

This four dimensional system was numerically integrated to produce a data set corresponding to the attractor shown in Fig. 1. There are four columns associated with the time evolution of *x*, *y*, *z*, and *v*, respectively. Parameter values were *b*=3 and *c*=0.05. The sampling time was s. Initial conditions were ,
, , and .

The observability coefficients for this four dimensional system are , , , , that is, the dynamical variables can be ranked as

[1] **A. Tamasevicius & A. Cenys**,
Synchronizing hyperchaos with a single variable, *Physical Review E*, **55**, 297, 1997.

[2] **O. E. Rössler**, An equation for hyperchaos,
*Physics Letters A*, **71**, 155, 1979.