Dynamical systems of different classes as models of the kicked nonlinear oscillator

Using the nonlinear dissipative kicked oscillator as an example, the corres pondence between the descriptions provided by model dynamical systems of di fferent classes is discussed. A detailed study of the approximate 1D map is undertaken: the period doubling is examined and the possibility of non-Fei genbaum period doubling is shown. Illustrations in the form of bifurcation diagrams and sets of iteration diagrams are given, the scaling properties a re demonstrated, and the tricritical points (the terminal points of the Fei genbaum critical curves) in parameter space are found. The congruity with t he properties of the corresponding 2D map, the Ikeda map, is studied. A des cription in terms of tricritical dynamics is found to be adequate only in p articular areas of parameter space.