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2-D Quadratic Maps and 3-D ODE Systems: A Rigorous Approach

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AuthorZeraoulia Elhadj Et Al
ISBN9789814307741
Published LanguageEnglish
Publication Year2010
PublisherWorld Scientific
BindingHardback
Original Price$130
Pages356
Ships By2-3 days

Description

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 H? non 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 H? non 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 Poincar? 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 Poincar? mapping in addition to other analytical methods.

About the author
Univ of Tebessa, Algeria

Additional information

Weight0.649 kg
Dimensions22.9 × 15.2 cm
Author

ISBN

Publisher

Pages

356

Ships By

2-3 days