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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
You can always find the topics here!Topics: Trivial solutions, Limit cycles, Subharmonics, Nonlinearity, Oscillation, Chaos theory, Contrapuntal motion, Linear systems, Oscillators, Mathematical manifolds
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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