Applying the DFT representation for describing the order-chaos transition in Hénon mapping dynamics

Abstract

The DFT representation is applied, to a ordered-chaotic finite-duration sequences set generated by the Hénon mapping, for describing the order-chaos transition. This representation has the advantage that it may be applied to a relatively shorter discret-time series. The bifurcation diagram is produced and the largest Lyapounov exponent is calculated for each time series of the set, showing a good agreement with the results obtained by the DFT representation. The threshold value of the control parameter for the order-chaos transition was determined to be A=1.0532.

13pages, 6figures