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Books > Science & Mathematics > Mathematics > Applied mathematics > Chaos theory
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2-d Quadratic Maps And 3-d Ode Systems: A Rigorous Approach (Hardcover)
Loot Price: R3,439
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2-d Quadratic Maps And 3-d Ode Systems: A Rigorous Approach (Hardcover)
Series: World Scientific Series on Nonlinear Science Series A, 73
Expected to ship within 12 - 17 working days
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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 H non 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 non
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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