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020 _a9783031571169
_9978-3-031-57116-9
024 7 _a10.1007/978-3-031-57116-9
_2doi
050 4 _aTA352-356
050 4 _aQC20.7.N6
072 7 _aTBJ
_2bicssc
072 7 _aGPFC
_2bicssc
072 7 _aSCI064000
_2bisacsh
072 7 _aTBJ
_2thema
072 7 _aGPFC
_2thema
100 1 _aLuo, Albert C. J.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_981241
245 1 0 _aTwo-dimensional Product-cubic Systems, Vol.II
_h[electronic resource] :
_bProduct-quadratic Vector Fields /
_cby Albert C. J. Luo.
250 _a1st ed. 2024.
264 1 _aCham :
_bSpringer Nature Switzerland :
_bImprint: Springer,
_c2024.
300 _aIX, 292 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 -- Self-linear and Crossing-cubic Vector Fields -- Self-quadratic and Crossing-cubic Vector Fields.
520 _aThis book, the sixth of 15 related monographs, discusses singularity and networks of equilibriums and 1-diemsnional flows in product quadratic and cubic systems. The author explains how, in the networks, equilibriums have source, sink and saddles with counter-clockwise and clockwise centers and positive and negative saddles, and the 1-dimensional flows includes source and sink flows, parabola flows with hyperbolic and hyperbolic-secant flows. He further describes how the singular equilibriums are saddle-source (sink) and parabola-saddles for the appearing bifurcations, and the 1-dimensional singular flows are the hyperbolic-to-hyperbolic-secant flows and inflection source (sink) flows for 1-dimensional flow appearing bifurcations, and the switching bifurcations are based on the infinite-equilibriums, including inflection-source (sink), parabola-source (sink), up-down and down-up upper-saddle (lower-saddle), up-down (down-up) sink-to-source and source-to-sink, hyperbolic and hyperbolic-secant saddles. The diagonal-inflection upper-saddle and lower-saddle infinite-equilibriums are for the double switching bifurcations. The networks of hyperbolic flows with connected saddle, source and center are presented, and the networks of the hyperbolic flows with paralleled saddle and center are also illustrated. Readers will learn new concepts, theory, phenomena, and analysis techniques. Product-quadratic and product cubic systems Self-linear and crossing-quadratic product vector fields Self-quadratic and crossing-linear product vector fields Hybrid networks of equilibriums and 1-dimensional flows Up-down and down-up saddle infinite-equilibriums Up-down and down-up sink-to-source infinite-equilibriums Inflection-source (sink) Infinite-equilibriums Diagonal inflection saddle infinite-equilibriums Infinite-equilibrium switching bifurcations Develops singularity and networks of equilibriums and 1-diemsnional flows in product-quadratic and cubic systems; Provides dynamics of product-quadratic/ product-cubic systems through equilibrium network and first integral manifolds; Discovers new switching bifurcations through infinite-equilibriums of up-down upper-saddles (lower-saddles). .
650 0 _aDynamics.
_965524
650 0 _aNonlinear theories.
_965525
650 0 _aEngineering mathematics.
_964145
650 0 _aEngineering
_xData processing.
650 0 _aMultibody systems.
_966046
650 0 _aVibration.
_966047
650 0 _aMechanics, Applied.
650 0 _aStochastic analysis.
_959375
650 0 _aMathematical analysis.
_964178
650 0 _aDynamical systems.
650 1 4 _aApplied Dynamical Systems.
_965530
650 2 4 _aMathematical and Computational Engineering Applications.
650 2 4 _aMultibody Systems and Mechanical Vibrations.
_966048
650 2 4 _aStochastic Analysis.
_959375
650 2 4 _aIntegral Transforms and Operational Calculus.
_967269
650 2 4 _aDynamical Systems.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031571152
776 0 8 _iPrinted edition:
_z9783031571176
776 0 8 _iPrinted edition:
_z9783031571183
856 4 0 _uhttps://doi.org/10.1007/978-3-031-57116-9
912 _aZDB-2-ENG
912 _aZDB-2-SXE
999 _c64858
_d64858