Periodic Solutions of Nonlinear Dynamical Systems : Numerical Computation, Stability, Bifurcation and Transition to Chaos
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 improv...
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| Auteur principal: | |
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| Format: | Livre numérique |
| Langue: | Anglais |
| Publié: |
Berlin [etc.] :
Springer
[20..].
Cham : Springer Nature |
| Collection: | Lecture notes in mathematics
1483 |
| Sujets: | |
| Accès en ligne: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Note: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Periodic solutions of nonlinear dynamical systems, numerical computation, stability, bifurcation and transition to chaos, Eduard Reithmeier, 1991, Berlin, Springer-Verlag, 1 volume (VI-171 pages), Lecture notes in mathematics, 3-540-54512-3 • Periodic Solutions of Nonlinear Dynamical Systems, Texte imprimé, 9783662163498 |
| Résumé: | 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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| Description: | Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| ISBN: | 9783540384274 (PDF) |
| ISSN: | 1617-9692 |
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