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020 _a9783031628108
_9978-3-031-62810-8
024 7 _a10.1007/978-3-031-62810-8
_2doi
050 4 _aQC718.5.W3
072 7 _aPHFP
_2bicssc
072 7 _aSCI055000
_2bisacsh
072 7 _aPHFP
_2thema
100 1 _aLuo, Albert C. J.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_981241
245 1 0 _aTwo-dimensional Crossing-Variable Cubic Nonlinear Systems
_h[electronic resource] /
_cby Albert C. J. Luo.
250 _a1st ed. 2024.
264 1 _aCham :
_bSpringer Nature Switzerland :
_bImprint: Springer,
_c2024.
300 _aX, 386 p. 33 illus., 32 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _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.
520 _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.
650 0 _aPlasma waves.
_969749
650 0 _aMultibody systems.
_966046
650 0 _aVibration.
_966047
650 0 _aMechanics, Applied.
650 0 _aDynamics.
_965524
650 0 _aNonlinear theories.
_965525
650 0 _aEngineering mathematics.
_964145
650 0 _aEngineering
_xData processing.
650 1 4 _aWaves, instabilities and nonlinear plasma dynamics.
_969750
650 2 4 _aMultibody Systems and Mechanical Vibrations.
_966048
650 2 4 _aApplied Dynamical Systems.
_965530
650 2 4 _aMathematical and Computational Engineering Applications.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031628092
776 0 8 _iPrinted edition:
_z9783031628115
776 0 8 _iPrinted edition:
_z9783031628122
856 4 0 _uhttps://doi.org/10.1007/978-3-031-62810-8
912 _aZDB-2-PHA
912 _aZDB-2-SXP
999 _c66686
_d66686