03266nam a22005055i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050001400172072001600186072002300202072001500225100008600240245015500326250001800481264006900499300006400568336002600632337002600658338003600684347002400720505022500744520126500969650003602234650002402270650002102294650003102315650002602346650003602372650002702408650003802435650002802473710003402501773002602535776003602561776003602597776003602633856004602669912001402715912001402729999001702743978-3-031-48472-8DE-He21320251030113252.0cr nn 008mamaa241031s2024    sz |    s    |||| 0|eng d  a97830314847289978-3-031-48472-87 a10.1007/978-3-031-48472-82doi 4aTA329-348 7aTBJ2bicssc 7aMAT0030002bisacsh 7aTBJ2thema1 aLuo, Albert C. J.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut98124110aTwo-dimensional Single-Variable Cubic Nonlinear Systems, Vol. Ih[electronic resource] :bA Self-univariate Cubic Vector Field /cby Albert C. J. Luo.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Springer,c2024.  aIX, 437 p. 32 illus., 31 illus. in color.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda0 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.  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. 0aEngineering mathematics.964145 0aMechanics, Applied. 0aDynamics.965524 0aNonlinear theories.965525 0aSystem theory.96651914aEngineering Mathematics.96414524aEngineering Mechanics.24aApplied Dynamical Systems.96553024aComplex Systems.9665202 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303148471108iPrinted edition:z978303148473508iPrinted edition:z978303148474240uhttps://doi.org/10.1007/978-3-031-48472-8  aZDB-2-ENG  aZDB-2-SXE  c64611d64611