03807nam a22005055i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001500153072001700168072002300185072001600208100007900224245010900303250001800412264006900430300006300499336002600562337002600588338003600614347002400650505018900674520184600863650001802709650002302727650001502750650002402765650001402789650002402803650002902827650003402856650005602890650004902946650003102995650006103026710003403087773002603121776003603147776003603183776003603219856004603255978-3-031-62810-8DE-He21320251030114941.0cr nn 008mamaa250212s2024    sz |    s    |||| 0|eng d  a97830316281087 a10.1007/978-3-031-62810-82doi 4aQC718.5.W3 7aPHFP2bicssc 7aSCI0550002bisacsh 7aPHFP2thema1 aLuo, Albert C. J.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut10aTwo-dimensional Crossing-Variable Cubic Nonlinear Systemsh[electronic resource] /cby Albert C. J. Luo.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Springer,c2024.  aX, 386 p. 33 illus., 32 illus. in color.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda0 aConstant and crossing-cubic vector fields -- Crossing-linear and crossing-cubic vector fields -- Crossing-quadratic and crossing-cubic Vector Field -- Two crossing-cubic vector fields.  aThis book is the fourth of 15 related monographs presents systematically a theory of crossing-cubic nonlinear systems. In this treatment, at least one vector field is crossing-cubic, and the other vector field can be constant, crossing-linear, crossing-quadratic, and crossing-cubic. For constant vector fields, the dynamical systems possess 1-dimensional flows, such as parabola and inflection flows plus third-order parabola flows. For crossing-linear and crossing-cubic systems, the dynamical systems possess saddle and center equilibriums, parabola-saddles, third-order centers and saddles (i.e, (3rd UP+:UP+)-saddle and (3rdUP-:UP-)-saddle) and third-order centers (i.e., (3rd DP+:DP-)-center, (3rd DP-, DP+)-center) . For crossing-quadratic and crossing-cubic systems, in addition to the first and third-order saddles and centers plus parabola-saddles, there are (3:2)parabola-saddle and double-inflection saddles, and for the two crossing-cubic systems, (3:3)-saddles and centers exist. Finally, the homoclinic orbits with centers can be formed, and the corresponding homoclinic networks of centers and saddles exist. Readers will learn new concepts, theory, phenomena, and analytic techniques, including · Constant and crossing-cubic systems · Crossing-linear and crossing-cubic systems · Crossing-quadratic and crossing-cubic systems · Crossing-cubic and crossing-cubic systems · Appearing and switching bifurcations · Third-order centers and saddles · Parabola-saddles and inflection-saddles · Homoclinic-orbit network with centers · Appearing bifurcations Develops equilibrium singularity and bifurcations in 2-dimensional self-cubic systems; Presents (1,3) and (3,3)-sink, source, and saddles; (1,2) and (3,2)-saddle-sink and saddle-source; (2,2)-double-saddles; Develops homoclinic networks of source, sink and saddles. 0aPlasma waves. 0aMultibody systems. 0aVibration. 0aMechanics, Applied. 0aDynamics. 0aNonlinear theories. 0aEngineering mathematics. 0aEngineeringxData processing.14aWaves, instabilities and nonlinear plasma dynamics.24aMultibody Systems and Mechanical Vibrations.24aApplied Dynamical Systems.24aMathematical and Computational Engineering Applications.2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303162809208iPrinted edition:z978303162811508iPrinted edition:z978303162812240uhttps://doi.org/10.1007/978-3-031-62810-8