Language:
English
繁體中文
Help
圖資館首頁
Login
Back
Switch To:
Labeled
|
MARC Mode
|
ISBD
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 systems
a 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 /
LDR
:02623nmm a2200277 a 4500
001
345431
003
WSP
005
20101122172728.0
006
m d
007
cr cuu|||uu|||
008
121106s2010 si a sb 001 0 eng d
020
$a
9789814307758 (electronic bk.)
020
$z
9789814307741
020
$z
9814307742
035
$a
00001109
050
4
$a
QA243
082
0 4
$a
512.74
$2
22
100
1
$a
Zeraoulia, Elhadj.
$3
575365
245
1 0
$a
2-D quadratic maps and 3-D ODE systems
$h
[electronic resource] :
$b
a rigorous approach /
$c
Elhadj Zeraoulia, Julien Clinton Sprott.
260
$a
Singapore ;
$a
Hackensack, N.J. :
$b
World Scientific Pub. Co.,
$c
c2010.
300
$a
xiii, 342 p. :
$b
ill.
490
1
$a
World scientific series on nonlinear science. Series A. Monographs and treatises,
$x
1793-1010 ;
$v
v. 73
504
$a
Includes bibliographical references (p. 315-336) and index.
520
$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 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.
533
$a
Electronic reproduction.
$b
Singapore :
$c
World Scientific Publishing Co.,
$d
2010.
$n
System requirements: Adobe Acrobat Reader.
$n
Mode of access: World Wide Web.
$n
Available to subscribing institutions.
650
0
$a
Forms, Quadratic.
$3
347694
650
0
$a
Differential equations, Linear.
$3
185864
650
0
$a
Bifurcation theory.
$3
185804
650
0
$a
Differentiable dynamical systems.
$3
183764
650
0
$a
Proof theory.
$3
190840
700
1
$a
Sprott, Julien C.
$3
575366
710
2
$a
World Scientific (Firm)
$3
575130
776
1
$z
9789814307741
776
1
$z
9814307742
830
0
$a
World Scientific series on nonlinear science.
$n
Series A,
$p
Monographs and treatises ;
$v
v. 45.
$3
437171
856
4 0
$u
http://www.worldscientific.com/worldscibooks/10.1142/7774#t=toc
based on 0 review(s)
ALL
電子館藏
Items
1 records • Pages 1 •
1
Inventory Number
Location Name
Item Class
Material type
Call number
Usage Class
Loan Status
No. of reservations
Opac note
Attachments
000000074962
電子館藏
1圖書
電子書
EB QA243 c2010
一般使用(Normal)
On shelf
0
1 records • Pages 1 •
1
Multimedia
Multimedia file
http://www.worldscientific.com/worldscibooks/10.1142/7774#t=toc
Reviews
Add a review
and share your thoughts with other readers
Export
pickup library
Processing
...
Change password
Login