On computing Poincare´ map by He´non method
P. Palaniyandi
Centre for Nonlinear dynamics, School of Physics, Bharathidasan University, Tiruchirapalli 620 024, India
Accepted 20 June 2007
Abstract
The trajectory of the autonomous chaotic system deviates from the original path leading to a deformation in its
attractor while calculating Poincare´ map using the method presented by He´non [He´non M. Physica D 1982;5:412].
Also, the Poincare´ map obtained is found to be the Poincare´ map of deformed attractor instead of the original attractor.
In order to overcome these drawbacks, this method is slightly modified by introducing an important change in the existing
algorithm. Then it is shown that the modified He´non method calculates the Poincare´ map of the original attractor
and it does not affect the system dynamics (attractor). The modified method is illustrated by means of the Lorenz and
Chua systems.
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