LEADER 04025nam 2200697 a 450 001 9910818249003321 005 20240516083347.0 010 $a1-283-14459-X 010 $a9786613144591 010 $a981-4307-75-0 035 $a(CKB)3360000000001383 035 $a(EBL)731209 035 $a(OCoLC)740446113 035 $a(SSID)ssj0000520625 035 $a(PQKBManifestationID)11364259 035 $a(PQKBTitleCode)TC0000520625 035 $a(PQKBWorkID)10514927 035 $a(PQKB)10171788 035 $a(MiAaPQ)EBC731209 035 $a(WSP)00001109 035 $a(Au-PeEL)EBL731209 035 $a(CaPaEBR)ebr10479795 035 $a(CaONFJC)MIL314459 035 $a(EXLCZ)993360000000001383 100 $a20110225d2010 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$a2-D quadratic maps and 3-D ODE systems $ea rigorous approach /$fElhadj Zeraoulia, Julien Clinton Sprott 205 $a1st ed. 210 $aSingapore ;$aHackensack, N.J. $cWorld Scientific Pub. Co.$dc2010 215 $a1 online resource (342 p.) 225 1 $aWorld Scientific series on nonlinear science. Series A, Monographs and treatises,$x1793-1010 ;$vv. 73 300 $aDescription based upon print version of record. 311 $a981-4307-74-2 320 $aIncludes bibliographical references and index. 327 $aPreface; Contents; Acknowledgements; 1. Tools for the rigorous proof of chaos and bifurcations; 2. 2-D quadratic maps: The invertible case; 3. Classification of chaotic orbits of the general 2-D quadratic map; 4. Rigorous proof of chaos in the double-scroll system; 5. Rigorous analysis of bifurcation phenomena; Bibliography; Index 330 $aThis book is based on research on the rigorous proof of chaos and bifurcations in 2-D quadratic maps, especially the invertible case such as the H?non map, and in 3-D ODE's, especially piecewise linear systems such as the Chua's circuit. In addition, the book covers some recent works in the field of general 2-D quadratic maps, especially their classification into equivalence classes, and finding regions for chaos, hyperchaos, and non-chaos in the space of bifurcation parameters. Following the main introduction to the rigorous tools used to prove chaos and bifurcations in the two representative systems, is the study of the invertible case of the 2-D quadratic map, where previous works are oriented toward H?non mapping. 2-D quadratic maps are then classified into 30 maps with well-known formulas. Two proofs on the regions for chaos, hyperchaos, and non-chaos in the space of the bifurcation parameters are presented using a technique based on the second-derivative test and bounds for Lyapunov exponents. Also included is the proof of chaos in the piecewise linear Chua's system using two methods, the first of which is based on the construction of Poincare map, and the second is based on a computer-assisted proof. Finally, a rigorous analysis is provided on the bifurcational phenomena in the piecewise linear Chua's system using both an analytical 2-D mapping and a 1-D approximated Poincare mapping in addition to other analytical methods. 410 0$aWorld Scientific series on nonlinear science.$nSeries A,$pMonographs and treatises ;$vv. 73. 606 $aForms, Quadratic 606 $aDifferential equations, Linear 606 $aBifurcation theory 606 $aDifferentiable dynamical systems 606 $aProof theory 615 0$aForms, Quadratic. 615 0$aDifferential equations, Linear. 615 0$aBifurcation theory. 615 0$aDifferentiable dynamical systems. 615 0$aProof theory. 676 $a515.352 700 $aZeraoulia$b Elhadj$01592935 701 $aSprott$b Julien C$042637 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910818249003321 996 $a2-D quadratic maps and 3-D ODE systems$93912821 997 $aUNINA