Global Aspects of the Dissipative Dynamical Systems. II: Periodic and Chaotic Responses in the Forced Lorenz System

Abstract

The response of the chaotic motion under a periodic perturbation is studied using the Lorenz model. The global phase diagram is obtained by computer simulations. The periodic response is characterized not only by the subharmonic frequency but also by the symmetry of the orbit in phase space. On the other hand, the chaotic response is characterized by two chaos parameters: fractal dimensions of the strange attractor and of the symbolic time series. The periodic perturbation induces a partially coherent response which is closely connected with the temporal intermittency appearing in the time series of the dynamical variables. Such a coherent behavior is understood in terms of the spectral analysis, fractal dimensions and the information entropy.