Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Zeitschrift für Naturforschung A

A Journal of Physical Sciences

Editor-in-Chief: Holthaus, Martin

Editorial Board: Fetecau, Corina / Kiefer, Claus

IMPACT FACTOR 2017: 1.414

CiteScore 2018: 1.15

SCImago Journal Rank (SJR) 2018: 0.370
Source Normalized Impact per Paper (SNIP) 2018: 0.431

See all formats and pricing
More options …
Volume 46, Issue 6


Heteroclinic Bifurcations and Invariant Manifolds in Rocking Block Dynamics

B. Bruhn / B. P. Koch
Published Online: 2014-06-02 | DOI: https://doi.org/10.1515/zna-1991-0603


A simple model of rigid block motion under the influence of external perturbations is discussed. For periodic forcings we prove the existence of Smale horseshoe chaos in the dynamics. For slender blocks a heteroclinic bifurcation condition is calculated exactly, i.e. without using perturbation methods. That means that our results are valid for arbitrary excitation amplitudes. Furthermore, analytical formulas for the first pieces of the stable and unstable manifolds are derived not only for periodically but also for transiently driven systems. In the case of small excitation and damping the Melnikov method is used to treat the full nonlinear problem

Keywords: Earthquake dynamics; Heteroclinic bifurcations; Melnikov method; Chaos

About the article

Received: 1991-02-13

Published Online: 2014-06-02

Published in Print: 1991-06-01

Citation Information: Zeitschrift für Naturforschung A, Volume 46, Issue 6, Pages 481–490, ISSN (Online) 1865-7109, ISSN (Print) 0932-0784, DOI: https://doi.org/10.1515/zna-1991-0603.

Export Citation

© 1946 – 2014: Verlag der Zeitschrift für Naturforschung. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

S. J. Hogan
Journal of Engineering Mechanics, 1994, Volume 120, Number 1, Page 11
International Journal of Bifurcation and Chaos, 2005, Volume 15, Number 06, Page 1901
B P Koch and B Bruhn
Journal of Physics A: Mathematical and General, 1992, Volume 25, Number 14, Page 3945
Yongkui Zou, Dan Zheng, and Shimin Chai
Journal of Mathematical Analysis and Applications, 2017, Volume 448, Number 2, Page 815
Jun Shen and Zhengdong Du
Zeitschrift für angewandte Mathematik und Physik, 2016, Volume 67, Number 3
A. Granados, S. J. Hogan, and T. M. Seara
SIAM Journal on Applied Dynamical Systems, 2012, Volume 11, Number 3, Page 801
R.H. Plaut, W.T. Fielder, and L.N. Virgin
Chaos, Solitons & Fractals, 1996, Volume 7, Number 2, Page 177

Comments (0)

Please log in or register to comment.
Log in