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Cross-well chaos and escape phenomena in driven oscillators

✍ Scribed by Wanda Szemplińska-Stupnicka

Publisher
Springer Netherlands
Year
1992
Tongue
English
Weight
970 KB
Volume
3
Category
Article
ISSN
0924-090X

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✦ Synopsis

The paper is devoted to the study of common features in regular and strange behavior of the three classic dissipative softening type driven oscillators: (a) twin-well potential system, (b) single-well potential unsymmetric system and (c) single-well potential symmetric system.

Computer simulations are followed by analytical approximalions. It is shown that tim mathematical techniques and physical concepts related to the theory of nonlinear oscillations are very useful in predicting bifurcations from regular, periodic responses m cross-well chaotic motions or to escape phenomena. The approximate analysis of periodic, resonant solutions and of period doubling or symmetry breaking instabilities in the Hill's type variational equation provides us with closed-form algebraic simple formulae: that is, the relationship between critical system parameter values, for which strange phenomena can be expected.

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