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Normal Forms, Melnikov Functions and Bifurcations of Limit Cycles
Dynamical system theory has developed rapidly over the past fifty years. It is a subject upon which the theory of limit cycles has a significant impact for both theoretical advances and practical solutions to problems. Hopf bifurcation from a center or a focus is integral to the theory of bifurcati...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
London :
Springer London : Imprint: Springer,
2012.
|
| Edición: | 1st ed. 2012. |
| Colección: | Applied Mathematical Sciences,
181 |
| Temas: | |
| Acceso en línea: | Texto Completo |
MARC
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| 001 | 978-1-4471-2918-9 | ||
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| 008 | 120419s2012 xxk| s |||| 0|eng d | ||
| 020 | |a 9781447129189 |9 978-1-4471-2918-9 | ||
| 024 | 7 | |a 10.1007/978-1-4471-2918-9 |2 doi | |
| 050 | 4 | |a QA843-871 | |
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| 072 | 7 | |a GPFC |2 thema | |
| 082 | 0 | 4 | |a 515.39 |2 23 |
| 100 | 1 | |a Han, Maoan. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Normal Forms, Melnikov Functions and Bifurcations of Limit Cycles |h [electronic resource] / |c by Maoan Han, Pei Yu. |
| 250 | |a 1st ed. 2012. | ||
| 264 | 1 | |a London : |b Springer London : |b Imprint: Springer, |c 2012. | |
| 300 | |a XII, 404 p. |b online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file |b PDF |2 rda | ||
| 490 | 1 | |a Applied Mathematical Sciences, |x 2196-968X ; |v 181 | |
| 505 | 0 | |a Hopf Bifurcation and Normal Form Computation -- Comparison of Methods for Computing Focus Values -- Application (I)-Hilbert's 16th Problem -- Application (II)-Practical Problems -- Fundamental Theory of the Melnikov Function Method -- Limit Cycle Bifurcations Near a Center -- Limit Cycles Near a Homoclinic or Heteroclinic Loop -- Finding More Limit Cycles Using Melnikov Functions -- Limit Cycle Bifurcations in Equivariant Systems. | |
| 520 | |a Dynamical system theory has developed rapidly over the past fifty years. It is a subject upon which the theory of limit cycles has a significant impact for both theoretical advances and practical solutions to problems. Hopf bifurcation from a center or a focus is integral to the theory of bifurcation of limit cycles, for which normal form theory is a central tool. Although Hopf bifurcation has been studied for more than half a century, and normal form theory for over 100 years, efficient computation in this area is still a challenge with implications for Hilbert's 16th problem. This book introduces the most recent developments in this field and provides major advances in fundamental theory of limit cycles. Split into two parts, the first focuses on the study of limit cycles bifurcating from Hopf singularity using normal form theory with later application to Hilbert's 16th problem, while the second considers near Hamiltonian systems using Melnikov function as the main mathematical tool. Classic topics with new results are presented in a clear and concise manner and are accompanied by the liberal use of illustrations throughout. Containing a wealth of examples and structured algorithms that are treated in detail, a good balance between theoretical and applied topics is demonstrated. By including complete Maple programs within the text, this book also enables the reader to reconstruct the majority of formulas provided, facilitating the use of concrete models for study. Through the adoption of an elementary and practical approach, this book will be of use to graduate mathematics students wishing to study the theory of limit cycles as well as scientists, across a number of disciplines, with an interest in the applications of periodic behavior. | ||
| 650 | 0 | |a Dynamical systems. | |
| 650 | 0 | |a Approximation theory. | |
| 650 | 0 | |a Differential equations. | |
| 650 | 0 | |a Computer software. | |
| 650 | 0 | |a Nonlinear Optics. | |
| 650 | 1 | 4 | |a Dynamical Systems. |
| 650 | 2 | 4 | |a Approximations and Expansions. |
| 650 | 2 | 4 | |a Differential Equations. |
| 650 | 2 | 4 | |a Mathematical Software. |
| 650 | 2 | 4 | |a Nonlinear Optics. |
| 700 | 1 | |a Yu, Pei. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 710 | 2 | |a SpringerLink (Online service) | |
| 773 | 0 | |t Springer Nature eBook | |
| 776 | 0 | 8 | |i Printed edition: |z 9781447158301 |
| 776 | 0 | 8 | |i Printed edition: |z 9781447129196 |
| 776 | 0 | 8 | |i Printed edition: |z 9781447129172 |
| 830 | 0 | |a Applied Mathematical Sciences, |x 2196-968X ; |v 181 | |
| 856 | 4 | 0 | |u https://doi.uam.elogim.com/10.1007/978-1-4471-2918-9 |z Texto Completo |
| 912 | |a ZDB-2-SMA | ||
| 912 | |a ZDB-2-SXMS | ||
| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||