You are not currently logged in.
Access JSTOR through your library or other institution:
If You Use a Screen ReaderThis content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Indeterminate Bifurcational Phenomena in Hardening Systems
Mohamed S. Soliman and J. M. T. Thompson
Proceedings: Mathematical, Physical and Engineering Sciences
Vol. 452, No. 1946 (Mar. 8, 1996), pp. 487-494
Published by: Royal Society
Stable URL: http://www.jstor.org/stable/52834
Page Count: 8
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Preview not available
Indeterminate bifurcations are emerging as an important ingredient of nonlinear dissipating dynamical systems. In this paper we show that indeterminate bifurcations with an unpredictable outcome are a typical ingredient of nonlinear hardening systems. Such phenomena are clearly important concepts in the theory of nonlinear resonance and their discovery complements the earlier work carried out on softening systems. As an illustrative example we examine the dynamics of a parametrically excited hardening system and show that when the trivial solution is located on a highly intertwined basin boundary, its loss of stability gives a dynamic jump whose outcome is indeterminate in the sense that we cannot predict on to which coexisting attractor the system will settle.
Proceedings: Mathematical, Physical and Engineering Sciences © 1996 Royal Society