Nonlinear Oscillations in Physical Systems

Author(s):  
George Adomian
1987 ◽  
Vol 54 (1) ◽  
pp. 250-251 ◽  
Author(s):  
Chihiro Hayashi ◽  
D. T. Mook

1965 ◽  
Vol 16 (7) ◽  
pp. 287-287
Author(s):  
C C Ritchie

1997 ◽  
Vol 07 (09) ◽  
pp. 2003-2033 ◽  
Author(s):  
Werner Lauterborn ◽  
Thomas Kurz ◽  
Ulrich Parlitz

The review gives and account of the historical development, the current state and possible future developments of experimental nonlinear physics, with emphasis on acoustics, hydrodynamics and optics. The concepts of nonlinear time-series analysis which are the basis of the analysis of experimental outcomes from nonlinear systems are explained and recent developments pertaining to such different fields as modeling, prediction, nonlinear noise reduction, detecting determinism, synchronization, and spatio-temporal time series are surveyed. An overview is given of experiments on acoustic cavitation, a field rich of nonlinear phenomena such as nonlinear oscillations, chaotic dynamics and structure formation, and one of the first physical systems to exhibit period-doubling and chaos in experiment.


1989 ◽  
Vol 111 (1) ◽  
pp. 115-116
Author(s):  
C. Hayashi ◽  
H. Saunders

1998 ◽  
Vol 08 (03) ◽  
pp. 521-533 ◽  
Author(s):  
L. N. Virgin ◽  
M. D. Todd ◽  
C. J. Begley ◽  
S. T. Trickey ◽  
E. H. Dowell

This paper addresses two relatively simple but fundamental questions in nonlinear oscillations: Given an arbitrary initial condition where will the trajectory go, and how long will it take to get there? These related questions are addressed from an experimental perspective where generating global transient behavior has received relatively little attention, despite the fact that a global view of transient behavior provides a much more complete description of the dynamics of a system than a traditional concentration on steady-state behavior. Three different physical systems are studied, each of which exhibits a specific behavior heavily influenced by transient global effects.


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