04747nam a22006735i 4500 978-3-031-57116-9 DE-He213 20251030113307.0 cr nn 008mamaa 241111s2024 sz | s |||| 0|eng d 9783031571169 978-3-031-57116-9 10.1007/978-3-031-57116-9 doi TA352-356 QC20.7.N6 TBJ bicssc GPFC bicssc SCI064000 bisacsh TBJ thema GPFC thema Luo, Albert C. J. author. aut http://id.loc.gov/vocabulary/relators/aut 81241 Two-dimensional Product-cubic Systems, Vol.II [electronic resource] : Product-quadratic Vector Fields / by Albert C. J. Luo. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. IX, 292 p. 33 illus., 32 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Constant and Crossing-cubic Vector Fields -- Self-linear and Crossing-cubic Vector Fields -- Self-quadratic and Crossing-cubic Vector Fields. This 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). . Dynamics. 65524 Nonlinear theories. 65525 Engineering mathematics. 64145 Engineering Data processing. Multibody systems. 66046 Vibration. 66047 Mechanics, Applied. Stochastic analysis. 59375 Mathematical analysis. 64178 Dynamical systems. Applied Dynamical Systems. 65530 Mathematical and Computational Engineering Applications. Multibody Systems and Mechanical Vibrations. 66048 Stochastic Analysis. 59375 Integral Transforms and Operational Calculus. 67269 Dynamical Systems. SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031571152 Printed edition: 9783031571176 Printed edition: 9783031571183 https://doi.org/10.1007/978-3-031-57116-9 ZDB-2-ENG ZDB-2-SXE 64858 64858