Periodic Solutions of Nonlinear Dynamical Systems: Numerical Computation, Stability, Bifurcation and Transition to Chaos: 1483 (Lecture Notes in Mathematics) - Softcover

Reithmeier, Eduard

 
9783540545125: Periodic Solutions of Nonlinear Dynamical Systems: Numerical Computation, Stability, Bifurcation and Transition to Chaos: 1483 (Lecture Notes in Mathematics)
Softcover
ISBN 10: 3540545123 ISBN 13: 9783540545125
Verlag: Springer, 2009

Inhaltsangabe

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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Reseña del editor

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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Verlag
Springer
Erscheinungsdatum
2009
Sprache
Englisch
ISBN 10 
3540545123
ISBN 13 
9783540545125
Einband
Tapa blanda
Anzahl der Seiten
180
Kontakt zum Hersteller
Nicht verfügbar
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9780387545127: Periodic Solutions of Nonlinear Dynamical Systems: Numerical Computation, Stability, Bifurcation, and Transition to Chaos (Lecture Notes in Mathematics)

Vorgestellte Ausgabe

ISBN 10:  0387545123 ISBN 13:  9780387545127
Softcover