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010   $a3-031-48472-X
024 7 $a10.1007/978-3-031-48472-8
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035   $a(MiAaPQ)EBC31747193
035   $a(Au-PeEL)EBL31747193
035   $a(DE-He213)978-3-031-48472-8
035   $a(EXLCZ)9936443154000041
100   $a20241031d2024      u|         0
101 0 $aeng
135   $aur|||||||||||
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aTwo-dimensional Single-Variable Cubic Nonlinear Systems, Vol. I $eA Self-univariate Cubic Vector Field /$fby Albert C. J. Luo
205   $a1st ed. 2024.
210  1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2024.
215   $a1 online resource (442 pages)
311 08$a3-031-48471-1 
327   $aChapter 1 Constant and Self-cubic Vector fields -- Chapter 2 Crossing-linear and Self-cubic Vector Fields -- Chapter 3 Crossing-quadratic and Self-Cubic Vector Fields -- Chapter 4 Two Single-variable Cubic Vector Fields.
330   $aThis book, the first of 15 related monographs, presents systematically a theory of cubic nonlinear systems with single-variable vector fields. The cubic vector fields are of self-variables and are discussed as the first part of the book. The 1-dimensional flow singularity and bifurcations are discussed in such cubic systems. The appearing and switching bifurcations of the 1-dimensional flows in such 2-dimensional cubic systems are for the first time to be presented. Third-order source and sink flows are presented, and the third-order parabola flows are also presented. The infinite-equilibriums are the switching bifurcations for the first and third-order source and sink flows, and the second-order saddle flows with the first and third-order parabola flows, and the inflection flows. The appearing bifurcations in such cubic systems includes saddle flows and third-order source (sink) flows, inflection flows and third-order up (down)-parabola flows. Develops the theory for 1-dimensonal flow singularity and bifurcations to elucidate dynamics of nonlinear systems; Provides a new research direction in nonlinear dynamics community; Shows how singularity and bifurcations occur not only for equilibriums and attractors but also for 1-dimensional flows.
606   $aEngineering mathematics
606   $aMechanics, Applied
606   $aDynamics
606   $aNonlinear theories
606   $aSystem theory
606   $aEngineering Mathematics
606   $aEngineering Mechanics
606   $aApplied Dynamical Systems
606   $aComplex Systems
615  0$aEngineering mathematics.
615  0$aMechanics, Applied.
615  0$aDynamics.
615  0$aNonlinear theories.
615  0$aSystem theory.
615 14$aEngineering Mathematics.
615 24$aEngineering Mechanics.
615 24$aApplied Dynamical Systems.
615 24$aComplex Systems.
676   $a003.75
700   $aLuo$b Albert C. J$0720985
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910903799003321
996   $aTwo-dimensional Single-Variable Cubic Nonlinear Systems, Vol. I$94272961
997   $aUNINA