Engineering and Computer Science Faculty Publications

Title

Bifurcations and Chaos in Parametrically Excited Single-Degree-of-Freedom Systems

Document Type

Article

Publication Date

1-1990

Journal Title

Nonlinear Dynamics

Volume

1

Issue

1

First Page

1

Last Page

21

DOI

10.1007/BF01857582

Abstract

The behavior of single-degree-of-freedom systems possessing quadratic and cubic nonlinearities subject to parametric excitation is investigated. Both fundamental and principal parametric resonances are considered. A global bifurcation diagram in the excitation amplitude and excitation frequency domain is presented showing different possible stable steady-state solutions (attractors). Fractal basin maps for fundamental and principal parametric resonances when three attractors coexist are presented in color. An enlargement of one region of the map for principal parametric resonance reveals a Cantor-like set of fractal boundaries. For some cases, both periodic and chaotic attractors coexist.

Keywords

Bifurcation theory, chaos, parametric vibrations, quadratic nonlinearity, cubic nonlinearity, fractal basin