LEADER 04296nam  22007215  450 
001 9910978380703321
005 20250212115412.0
010   $a9783031628108
010   $a3031628101
024 7 $a10.1007/978-3-031-62810-8
035   $a(CKB)37515644400041
035   $a(MiAaPQ)EBC31903254
035   $a(Au-PeEL)EBL31903254
035   $a(OCoLC)1499354023
035   $a(DE-He213)978-3-031-62810-8
035   $a(EXLCZ)9937515644400041
100   $a20250212d2024      u|         0
101 0 $aeng
135   $aur|||||||||||
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aTwo-dimensional Crossing-Variable Cubic Nonlinear Systems /$fby Albert C. J. Luo
205   $a1st ed. 2024.
210  1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2024.
215   $a1 online resource (338 pages)
311 08$a9783031628092 
311 08$a3031628098 
327   $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.
330   $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.
606   $aPlasma waves
606   $aMultibody systems
606   $aVibration
606   $aMechanics, Applied
606   $aDynamics
606   $aNonlinear theories
606   $aEngineering mathematics
606   $aEngineering$xData processing
606   $aWaves, instabilities and nonlinear plasma dynamics
606   $aMultibody Systems and Mechanical Vibrations
606   $aApplied Dynamical Systems
606   $aMathematical and Computational Engineering Applications
615  0$aPlasma waves.
615  0$aMultibody systems.
615  0$aVibration.
615  0$aMechanics, Applied.
615  0$aDynamics.
615  0$aNonlinear theories.
615  0$aEngineering mathematics.
615  0$aEngineering$xData processing.
615 14$aWaves, instabilities and nonlinear plasma dynamics.
615 24$aMultibody Systems and Mechanical Vibrations.
615 24$aApplied Dynamical Systems.
615 24$aMathematical and Computational Engineering Applications.
676   $a530.44
700   $aLuo$b Albert C. J$0720985
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910978380703321
996   $aTwo-Dimensional Crossing-Variable Cubic Nonlinear Systems$94323204
997   $aUNINA