2-D Quadratic Maps and 3-D ODE Systems: A Rigorous Approach (World Scientific Series on Nonlinear Science, Series A) (World Scientific Series on . . . Series in Nonlinear Science, Series a) - Couverture souple

Elhadj, Zeraoulia Elhadj

Couverture souple

ISBN 10 : 9814307742 ISBN 13 : 9789814307741

Editeur : World Scientific Publishing Company, 2010

Synopsis

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A propos du livre

Présentation de l'éditeur :

This book is based on research on the rigorous proof of chaos and bifurcations in 2-D quadratic maps, especially the invertible case such as the Hénon map, and in 3-D ODE's, especially piecewise linear systems such as the Chua's circuit. In addition, the book covers some recent works in the field of general 2-D quadratic maps, especially their classification into equivalence classes, and finding regions for chaos, hyperchaos, and non-chaos in the space of bifurcation parameters.

Following the main introduction to the rigorous tools used to prove chaos and bifurcations in the two representative systems, is the study of the invertible case of the 2-D quadratic map, where previous works are oriented toward Hénon mapping. 2-D quadratic maps are then classified into 30 maps with well-known formulas. Two proofs on the regions for chaos, hyperchaos, and non-chaos in the space of the bifurcation parameters are presented using a technique based on the second-derivative test and bounds for Lyapunov exponents. Also included is the proof of chaos in the piecewise linear Chua's system using two methods, the first of which is based on the construction of Poincaré map, and the second is based on a computer-assisted proof. Finally, a rigorous analysis is provided on the bifurcational phenomena in the piecewise linear Chua's system using both an analytical 2-D mapping and a 1-D approximated Poincaré mapping in addition to other analytical methods.

Revue de presse :

"As a reader in favor of tradition in mathematics, I find attractive the approach based on examples."-- Mathematical Reviews

"The book is generously illustrated; each chapter contains a short section with exercises for independent study. The monograph concludes with an exhaustive list of references and a concise index. It is a useful source for information specialists and graduate students working with the theory and applications of dynamical systems." --Zentralblatt MATH

À propos de cette édition

• Éditeur: World Scientific Publishing Company
• Date d'édition: 2010
• ISBN 10: 9814307742
• ISBN 13: 9789814307741
• Reliure: Broché
• Nombre de pages: 356