COMMON DYNAMICAL FEATURES OF PERIODICALLY DRIVEN STRICTLY DISSIPATIVE OSCILLATORS

Abstract

Periodically driven strictly dissipative nonlinear oscillators in general possess a recurring bifurcation structure in parameter space. It consists of slightly modified versions of a basic pattern of bifurcation curves that was found to be essentially the same for many different oscillators. The periodic orbits involved in these bifurcation scenarios also possess common topological properties characterized in terms of their torsion numbers and the way they are connected when parameters are varied. In this paper, this typical bifurcation structure of periodically driven strictly dissipative oscillators will be presented and discussed in terms of examples from Duffing’s equation. Furthermore a family of two-dimensional maps is given that models (strictly) dissipative oscillators and shows essential features of the bifurcation pattern found.