ENGLISH

Periodic Solutions of Nonlinear Dynamical Systems: Numerical Computation, Stability, Bifurcation and Transition to Chaos

By Eduard Reithmeier (auth.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
1991
ISBN
3540545123, 9783540545125, 3540545123-:, 0387545123
DOI
10.1007/BFb0094521
LCC
QA3 .L28 no. 1483,QA372 .L28 no. 1483
Open Library ID
OL1551885M
Language
english
Format
DJVU
Filesize
1 MB (1063524 bytes)
Series
Lecture Notes in Mathematics 1483
Edition
1
Pages
174\178
Library
Kolxo3
DPI
300
Time added
2009-07-20 03:45:11
Analysis; Appl.Mathematics/Computational Methods o

Description

Limit cycles or, more general, periodic solutions of nonlinear dynamical systems occur in many different fields of application. Although, there is extensive literature on periodic solutions, in particular on existence theorems, the connection to physical and technical applications needs to be improved. The bifurcation behavior of periodic solutions by means of parameter variations plays an important role in transition to chaos, so numerical algorithms are necessary to compute periodic solutions and investigate their stability on a numerical basis. From the technical point of view, dynamical systems with discontinuities are of special interest. The discontinuities may occur with respect to the variables describing the configuration space manifold or/and with respect to the variables of the vector-field of the dynamical system. The multiple shooting method is employed in computing limit cycles numerically, and is modified for systems with discontinuities. The theory is supported by numerous examples, mainly from the field of nonlinear vibrations. The text addresses mathematicians interested in engineering problems as well as engineers working with nonlinear dynamics.

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