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

Af: Julien Clinton Sprott, Zeraoulia Elhadj Engelsk Hardback

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

Af: Julien Clinton Sprott, Zeraoulia Elhadj Engelsk Hardback
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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.
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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.
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Se mere i:
Produktdetaljer
Sprog: Engelsk
Sider: 356
ISBN-13: 9789814307741
Indbinding: Hardback
Udgave:
ISBN-10: 9814307742
Kategori: Kaosteori
Udg. Dato: 9 jul 2010
Længde: 24mm
Bredde: 166mm
Højde: 236mm
Forlag: World Scientific Publishing Co Pte Ltd
Oplagsdato: 9 jul 2010
Forfatter(e): Julien Clinton Sprott, Zeraoulia Elhadj
Forfatter(e) Julien Clinton Sprott, Zeraoulia Elhadj

Kategori Kaosteori

ISBN-13 9789814307741

Sprog Engelsk

Indbinding Hardback

Sider 356

Udgave

Længde 24mm

Bredde 166mm

Højde 236mm

Udg. Dato 9 jul 2010

Oplagsdato 9 jul 2010

Forlag World Scientific Publishing Co Pte Ltd