the Lorenz attractor

A question on the distortion of the dynamic system parameters estimation using a time variation of the single component after exposing recursive filters with different order and with different cut-off frequency is analyzed. The Lorenz system is used as a test dynamic system for comparative evaluation of the correlation dimension and the dimension of the system state vector in the case of recursive filtering.

The paper deals with a parametric oscillator composed of three LC-circuits and a quadratic nonlinear reactive element built on the basis of an operational amplifier and an analog multiplier; the equations for amplitudes of the interacting modes are derived. Motivation is a desire to implement the mechanism of parametric interaction of oscillatory modes giving rise to emergence of a strange attractor of Lorenz type without distortions introduced by nonlinearities of order three and higher.