2-d Quadratic Maps And 3-d Ode Systems: A Rigorous Approach

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Zeraoulia Elhadj (Univ Of Tebessa, Algeria) Julien Clinton Sprott (Univ Of Wisconsin-madison, Usa)

2-d Quadratic Maps And 3-d Ode Systems

A Rigorous Approach

Zeraoulia Elhadj (Univ Of Tebessa, Algeria), Julien Clinton Sprott (Univ Of Wisconsin-madison, Usa)

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English

World Scientific Publishing Co Pte Ltd
09 July 2010

Chaos theory

Series: World Scientific Series on Nonlinear Science Series A

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 Henon 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 Henon 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 Poincare 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 Poincare mapping in addition to other analytical methods.

By: Zeraoulia Elhadj (Univ Of Tebessa Algeria), Julien Clinton Sprott (Univ Of Wisconsin-madison, Usa)
Imprint: World Scientific Publishing Co Pte Ltd
Country of Publication: Singapore
Volume: 73
Dimensions: Height: 249mm, Width: 165mm, Spine: 18mm
Weight: 617g
ISBN: 9789814307741
ISBN 10: 9814307742
Series: World Scientific Series on Nonlinear Science Series A
Pages: 356
Publication Date: 09 July 2010
Audience: College/higher education , Professional and scholarly , Primary , Undergraduate
Format: Hardback
Publisher's Status: Active

Reviews for 2-d Quadratic Maps And 3-d Ode Systems: A Rigorous Approach

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