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2-D quadratic maps and 3-D ODE syste...

Sprott, Julien C.

2-D quadratic maps and 3-D ODE systemsa rigorous approach /

Record Type:	Electronic resources : Monograph/item
Title/Author:	2-D quadratic maps and 3-D ODE systemsElhadj Zeraoulia, Julien Clinton Sprott.
Reminder of title:	a rigorous approach /
Author:	Zeraoulia, Elhadj.
other author:	Sprott, Julien C.
Published:	Singapore ;World Scientific Pub. Co.,c2010.
Description:	xiii, 342 p. :ill.
Subject:	Forms, Quadratic.
Online resource:	http://www.worldscientific.com/worldscibooks/10.1142/7774#t=toc
ISBN:	9789814307758 (electronic bk.)

2-D quadratic maps and 3-D ODE systemsa rigorous approach /
Zeraoulia, Elhadj.

2-D quadratic maps and 3-D ODE systemsa rigorous approach /[electronic resource] :Elhadj Zeraoulia, Julien Clinton Sprott. - Singapore ;World Scientific Pub. Co.,c2010. - xiii, 342 p. :ill. - World scientific series on nonlinear science. Series A. Monographs and treatises,v. 731793-1010 ;. - World Scientific series on nonlinear science.Series A,Monographs and treatises ;v. 45..

Includes bibliographical references (p. 315-336) and index.

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幯on 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幯on 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.

Electronic reproduction.
Singapore :
World Scientific Publishing Co.,
2010.

System requirements: Adobe Acrobat Reader.

ISBN: 9789814307758 (electronic bk.)Subjects--Topical Terms:

347694
Forms, Quadratic.

LC Class. No.: QA243

Dewey Class. No.: 512.74

2-D quadratic maps and 3-D ODE systemsa rigorous approach /
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