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019 714877594|a741454360|a816846449
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020 9814307750|q(electronic book)
020 128314459X
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020 |z9789814307741
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100 1 Zeraoulia, Elhadj.|0https://id.loc.gov/authorities/names/
nb2010024163
245 10 2-D quadratic maps and 3-D ODE systems :|ba rigorous
approach /|cElhadj Zeraoulia, Julien Clinton Sprott.
264 1 Singapore ;|aHackensack, N.J. :|bWorld Scientific,|c[2010]
264 4 |c©2010
300 1 online resource (xiii, 342 pages) :|billustrations.
336 text|btxt|2rdacontent
337 computer|bc|2rdamedia
338 online resource|bcr|2rdacarrier
340 |gpolychrome|2rdacc
347 text file|2rdaft
490 1 World scientific series on nonlinear science. Series A.
Monographs and treatises,|x1793-1010 ;|vv. 73
504 Includes bibliographical references and index.
505 0 1. Tools for the rigorous proof of chaos and bifurcations.
1.1. Introduction. 1.2. A chain of rigorous proof of
chaos. 1.3. Poincare map technique. 1.4. The method of
fixed point index. 1.5. Smale's horseshoe map. 1.6. The
Sil'nikov criterion for the existence of chaos. 1.7. The
Marotto theorem. 1.8. The verified optimization technique.
1.9. Shadowing lemma. 1.10. Method based on the second-
derivative test and bounds for Lyapunov exponents. 1.11.
The Wiener and Hammerstein cascade models. 1.12. Methods
based on time series analysis. 1.13. A new chaos detector.
1.14. Exercises -- 2. 2-D quadratic maps : The invertible
case. 2.1. Introduction. 2.2. Equivalences in the general
2-D quadratic maps. 2.3. Invertibility of the map. 2.4.
The Henon map. 2.5. Methods for locating chaotic regions
in the Henon map. 2.6. Bifurcation analysis. 2.7.
Exercises -- 3. Classification of chaotic orbits of the
general 2-D quadratic map. 3.1. Analytical prediction of
system orbits. 3.2. A zone of possible chaotic orbits.
3.3. Boundary between different attractors. 3.4. Finding
chaotic and nonchaotic attractors. 3.5. Finding
hyperchaotic attractors. 3.6. Some criteria for finding
chaotic orbits. 3.7. 2-D quadratic maps with one
nonlinearity. 3.8. 2-D quadratic maps with two
nonlinearities. 3.9. 2-D quadratic maps with three
nonlinearities. 3.10. 2-D quadratic maps with four
nonlinearities. 3.11. 2-D quadratic maps with five
nonlinearities. 3.12. 2-D quadratic maps with six
nonlinearities. 3.13. Numerical analysis -- 4. Rigorous
proof of chaos in the double-scroll system. 4.1.
Introduction. 4.2. Piecewise linear geometry and its real
Jordan form. 4.3. The dynamics of an orbit in the double-
scroll. 4.4. Poincare map [symbol]. 4.5. Method 1 :
Sil'nikov criteria. 4.6. Subfamilies of the double-scroll
family. 4.7. The geometric model. 4.8. Method 2 : The
computer-assisted proof. 4.9. Exercises -- 5. Rigorous
analysis of bifurcation phenomena. 5.1. Introduction. 5.2.
Asymptotic stability of equilibria. 5.3. Types of chaotic
attractors in the double-scroll. 5.4. Method 1 : Rigorous
mathematical analysis. 5.5. Method 2 : One-dimensional
Poincare map. 5.6. Exercises.
520 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 Hňon 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 Hňon 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.
588 0 Print version record.
590 eBooks on EBSCOhost|bEBSCO eBook Subscription Academic
Collection - North America
650 0 Forms, Quadratic.|0https://id.loc.gov/authorities/subjects
/sh85050828
650 0 Differential equations, Linear.|0https://id.loc.gov/
authorities/subjects/sh85037903
650 0 Bifurcation theory.|0https://id.loc.gov/authorities/
subjects/sh85013940
650 0 Differentiable dynamical systems.|0https://id.loc.gov/
authorities/subjects/sh85037882
650 0 Proof theory.|0https://id.loc.gov/authorities/subjects/
sh85107437
650 7 Forms, Quadratic.|2fast|0https://id.worldcat.org/fast/
932985
650 7 Differential equations, Linear.|2fast|0https://
id.worldcat.org/fast/893468
650 7 Bifurcation theory.|2fast|0https://id.worldcat.org/fast/
831564
650 7 Differentiable dynamical systems.|2fast|0https://
id.worldcat.org/fast/893426
650 7 Proof theory.|2fast|0https://id.worldcat.org/fast/1078942
655 0 Electronic books.
655 4 Electronic books.
700 1 Sprott, Julien C.|0https://id.loc.gov/authorities/names/
n80163145
776 08 |iPrint version:|aZeraoulia, Elhadj.|t2-D quadratic maps
and 3-D ODE systems.|dSingapore ; Hackensack, N.J. : World
Scientific, ©2010|z9789814307741|w(OCoLC)613429472
830 0 World Scientific series on nonlinear science.|nSeries A,
|pMonographs and treatises ;|0https://id.loc.gov/
authorities/names/no94008495|vv. 73.
856 40 |uhttps://rider.idm.oclc.org/login?url=http://
search.ebscohost.com/login.aspx?direct=true&scope=site&
db=nlebk&AN=374914|zOnline eBook. Access restricted to
current Rider University students, faculty, and staff.
856 42 |3Instructions for reading/downloading this eBook|uhttp://
guides.rider.edu/ebooks/ebsco
901 MARCIVE 20231220
948 |d20160616|cEBSCO|tebscoebooksacademic|lridw
994 92|bRID
