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Home Academics Nonlinear Science, Chaos and Dynamical Systems 2-d Quadratic Maps And 3-d Ode Systems: A Rigorous Approach: 73 (World Scientific Series on Nonlinear Science Series A)
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2-d Quadratic Maps And 3-d Ode Systems: A Rigorous Approach: 73 (World Scientific Series on Nonlinear Science Series A)
by Zeraoulia Elhadj and Julien Clinton Sprott
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AuthorZeraoulia Elhadj and Julien Clinton Sprott
Publisher World Scientific Publishing Co Pte Ltd
SynopsisThis 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 Hnon 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 invertibe case of the 2-D quadratic map, where previous works are oriented toward Hnon 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 Poincar 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 Poincar mapping in addition to other analytical methods.
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Binding: Paperback
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Specifications
Language: English
Publisher: World Scientific Publishing Co Pte Ltd
Pages: 356 pages
Binding: Paperback
ISBN: 9789814307741
Category: Nonlinear Science, Chaos and Dynamical Systems
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