Zeraoulia Elhadj Et Al 2-D Quadratic Maps And 3-D Ode Systems: A Rigorous Approach 9789814307741

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Автор: Zeraoulia Elhadj Et Al
Название: 2-D Quadratic Maps And 3-D Ode Systems: A Rigorous Approach
ISBN: 9789814307741
Издательство: World Scientific Publishing
Классификация:

Теория хаоса

ISBN-10: 9814307742
Обложка/Формат: Hardback
Страницы: 356
Вес: 0.64 кг.
Дата издания: 09.07.2010
Серия: World Scientific Series On Nonlinear Science Series A
Язык: English
Иллюстрации: Black & white illustrations, black & white tables, figures
Размер: 236 x 166 x 24
Читательская аудитория: General (us: trade)
Основная тема: Nonlinear Science, Chaos & Dynamical Systems / Nonlinear Science, Chaos & Dynamical Systems
Ссылка на Издательство: Link
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Поставляется из: Англии
Описание: 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 ODEs, especially piecewise linear systems such as the Chuas 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 Chuas 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 Chuas system using both an analytical 2-D mapping and a 1-D approximated Poincar mapping in addition to other analytical methods.

2-D Quadratic Maps And 3-D Ode Systems: A Rigorous Approach, Zeraoulia Elhadj Et Al