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Rössler map

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In 1979 Otto Rössler found the inspiration from a Taffy-Pulling machine to his Non-linear three-dimensional deterministic dynamical system. This system behaves much as the Lorenz attractor for specific values of the parameters and was found to follow the period-two doubling route to chaos like the Logistic map. The Rössler system having only one linearity appears like:

The Lorenz attractor is defined by a set of three coupled nonlinear differential equations:

${dx \over dt} = -y -z$

${dy \over dt} = x + ay$

${dz \over dt} = b+z(x-c)$

Numerical integration shows that the system exhibits a strange attractor for a=b=0.2 and c=5.7.

References

Steven H. Strogatz, Nonlinear Dynamics and Chaos, Perseus publishing 1994.
O.E. Rössler, An Equation for Hyperchaos, Phys.let. Vol.71A no 2,3 1979.

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09-23-2007 01:00:40
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