Crises in Mechanical Systems
In mechanical systems nonlinear effects due to stick slip and backlash are often observed. If such systems are harmonically driven, then besides well known bifurcation phenomena also sudden changes of the chaotic dynamics occur. These types of qualitative change of system’s behavior, the so-called crises, result from a collision between an unstable periodic orbit and a chaotic attractor. Different crises phenomena are discussed and it is demonstrated how the occurrence of crises can be determined numerically.
KeywordsPeriodic Solution Bifurcation Diagram Chaotic Attractor Pitchfork Bifurcation Unstable Solution
Unable to display preview. Download preview PDF.
- Y. Ueda. Explosion of strange attractors exhibited by duffing's equation. Annals of the New York Academy of Sciences,357 (1980) 422–434.Google Scholar
- C. Grebogi, E. Ott, and J. Yorke. Crises, sudden changes in chaotic attractors, and transient chaos. Physica D,7 (1983) 181–200.Google Scholar
- C. Wilmers. Verzweigungsphänomene in mechanischen Oszillatoren. Diplomarbeit DIPL-24. Stuttgart: Universität Stuttgart, Institut B für Mechanik 1988.Google Scholar
- C.S. Hsu and W.H. Zhu. A simplicial mapping method for locating the zeros of a function. Quarterly of Applied Mathematics (1984) 41 — 59.Google Scholar