LEADER 05053nam  22008415  450 
001 9910906198203321
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010   $a9783031571169
010   $a3031571169
024 7 $a10.1007/978-3-031-57116-9
035   $a(CKB)36549575800041
035   $a(MiAaPQ)EBC31776506
035   $a(Au-PeEL)EBL31776506
035   $a(DE-He213)978-3-031-57116-9
035   $a(EXLCZ)9936549575800041
100   $a20241111d2024      u|         0
101 0 $aeng
135   $aur|||||||||||
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aTwo-dimensional Product-cubic Systems, Vol.II $eProduct-quadratic Vector Fields /$fby Albert C. J. Luo
205   $a1st ed. 2024.
210  1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2024.
215   $a1 online resource (300 pages)
225 1 $aPalgrave Studies in the History of Science and Technology Series
300   $aIncludes index.
311 08$a9783031571152 
311 08$a3031571150 
327   $aConstant and Crossing-cubic Vector Fields -- Self-linear and Crossing-cubic Vector Fields -- Self-quadratic and Crossing-cubic Vector Fields.
330   $aThis book, the sixth of 15 related monographs, discusses singularity and networks of equilibriums and 1-diemsnional flows in product quadratic and cubic systems. The author explains how, in the networks, equilibriums have source, sink and saddles with counter-clockwise and clockwise centers and positive and negative saddles, and the 1-dimensional flows includes source and sink flows, parabola flows with hyperbolic and hyperbolic-secant flows. He further describes how the singular equilibriums are saddle-source (sink) and parabola-saddles for the appearing bifurcations, and the 1-dimensional singular flows are the hyperbolic-to-hyperbolic-secant flows and inflection source (sink) flows for 1-dimensional flow appearing bifurcations, and the switching bifurcations are based on the infinite-equilibriums, including inflection-source (sink), parabola-source (sink), up-down and down-up upper-saddle (lower-saddle), up-down (down-up) sink-to-source and source-to-sink, hyperbolic and hyperbolic-secant saddles. The diagonal-inflection upper-saddle and lower-saddle infinite-equilibriums are for the double switching bifurcations. The networks of hyperbolic flows with connected saddle, source and center are presented, and the networks of the hyperbolic flows with paralleled saddle and center are also illustrated. Readers will learn new concepts, theory, phenomena, and analysis techniques. Product-quadratic and product cubic systems Self-linear and crossing-quadratic product vector fields Self-quadratic and crossing-linear product vector fields Hybrid networks of equilibriums and 1-dimensional flows Up-down and down-up saddle infinite-equilibriums Up-down and down-up sink-to-source infinite-equilibriums Inflection-source (sink) Infinite-equilibriums Diagonal inflection saddle infinite-equilibriums Infinite-equilibrium switching bifurcations Develops singularity and networks of equilibriums and 1-diemsnional flows in product-quadratic and cubic systems; Provides dynamics of product-quadratic/ product-cubic systems through equilibrium network and first integral manifolds; Discovers new switching bifurcations through infinite-equilibriums of up-down upper-saddles (lower-saddles). .
410  0$aPalgrave studies in the history of science and technology.
606   $aDynamics
606   $aNonlinear theories
606   $aEngineering mathematics
606   $aEngineering$xData processing
606   $aMultibody systems
606   $aVibration
606   $aMechanics, Applied
606   $aStochastic analysis
606   $aMathematical analysis
606   $aDynamics
606   $aApplied Dynamical Systems
606   $aMathematical and Computational Engineering Applications
606   $aMultibody Systems and Mechanical Vibrations
606   $aStochastic Analysis
606   $aIntegral Transforms and Operational Calculus
606   $aDynamical Systems
615  0$aDynamics.
615  0$aNonlinear theories.
615  0$aEngineering mathematics.
615  0$aEngineering$xData processing.
615  0$aMultibody systems.
615  0$aVibration.
615  0$aMechanics, Applied.
615  0$aStochastic analysis.
615  0$aMathematical analysis.
615  0$aDynamics.
615 14$aApplied Dynamical Systems.
615 24$aMathematical and Computational Engineering Applications.
615 24$aMultibody Systems and Mechanical Vibrations.
615 24$aStochastic Analysis.
615 24$aIntegral Transforms and Operational Calculus.
615 24$aDynamical Systems.
676   $a512.82
700   $aLuo$b Albert C. J.$0720985
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910906198203321
996   $aTwo-dimensional Product-cubic Systems, Vol.II$94295781
997   $aUNINA