03287nam a22004815i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001500153072001700168072002300185072001600208100007900224245011900303250001800422264006900440300006300509336002600572337002600598338003600624347002400660505016700684520145900851650001802310650001402328650002402342650002402366650002302390650001502413650005602428650003102484650002702515650004902542710003402591773002602625776003602651776003602687776003602723856004602759978-3-031-57112-1DE-He21320251030113302.0cr nn 008mamaa241108s2024    sz |    s    |||| 0|eng d  a97830315711217 a10.1007/978-3-031-57112-12doi 4aQC718.5.W3 7aPHFP2bicssc 7aSCI0550002bisacsh 7aPHFP2thema1 aLuo, Albert C. J.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut10aTwo-dimensional Self-independent Variable Cubic Nonlinear Systemsh[electronic resource] /cby Albert C. J. Luo.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Springer,c2024.  aX, 275 p. 33 illus., 32 illus. in color.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda0 aConstant and Self-Cubic Vector fields -- Self-linear and Self-cubic vector fields -- Self-quadratic and self-cubic vector fields  -- Two self-cubic vector fields.  aThis book is the third of 15 related monographs, presents systematically a theory of self-cubic nonlinear systems. Here, at least one vector field is self-cubic, the other vector fields can be constant, self-linear, self-quadratic, and self-cubic. For constant vector fields in this book, the dynamical systems possess 1-dimensional flows, such as source, sink and saddle flows, plus third-order source and sink flows. For self-linear and self-cubic systems, the dynamical systems possess source, sink, and saddle equilibriums, saddle-source and saddle-sink equilibriums, third-order source and sink (i.e., ( 3rdSO:SO)-source, ( 3rdSI:SI)-sink) and third-order saddle (i.e., (3rdSO:SI)-saddle, 3rdSI:SO)-saddle). For self-quadratic and self-cubic systems, in addition to the first and third-order source, sink, saddles plus saddle-source, saddle-sink, there are (3,2)-saddle-sink, (3,2)-saddle-source and double-saddles, and for the two self-cubic systems, double third-order source, sink and saddles exist. Finally, the authors describes thar the homoclinic orbits without cen-ters can be formed, and the corresponding homoclinic networks of source, sink and saddles exist. • 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. 0aDynamics. 0aNonlinear theories. 0aMechanics, Applied. 0aMultibody systems. 0aVibration.14aWaves, instabilities and nonlinear plasma dynamics.24aApplied Dynamical Systems.24aEngineering Mechanics.24aMultibody Systems and Mechanical Vibrations.2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303157111408iPrinted edition:z978303157113808iPrinted edition:z978303157114540uhttps://doi.org/10.1007/978-3-031-57112-1