03980nam a22005895i 4500 978-3-031-57092-6 DE-He213 20251030113255.0 cr nn 008mamaa 241101s2024 sz | s |||| 0|eng d 9783031570926 978-3-031-57092-6 10.1007/978-3-031-57092-6 doi QC718.5.W3 PHFP bicssc SCI055000 bisacsh PHFP thema Luo, Albert C. J. author. aut http://id.loc.gov/vocabulary/relators/aut 81241 Two-dimensional Product-Cubic Systems, Vol. I [electronic resource] : Constant and Linear Vector Fields / by Albert C. J. Luo. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. X, 250 p. 46 illus., 45 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Constant and Product-Cubic Systems -- Self-linear and Product-cubic systems -- Crossing-linear and Product-cubic systems. This book, the fifth of 15 related monographs, presents systematically a theory of product-cubic nonlinear systems with constant and single-variable linear vector fields. The product-cubic vector field is a product of linear and quadratic different univariate functions. The hyperbolic and hyperbolic-secant flows with directrix flows in the cubic product system with a constant vector field are discussed first, and the cubic product systems with self-linear and crossing-linear vector fields are discussed. The inflection-source (sink) infinite equilibriums are presented for the switching bifurcations of a connected hyperbolic flow and saddle with hyperbolic-secant flow and source (sink) for the connected the separated hyperbolic and hyperbolic-secant flows. The inflection-sink and source infinite-equilibriums with parabola-saddles are presented for the switching bifurcations of a separated hyperbolic flow and saddle with a hyperbolic-secant flow and center. Readers learn new concepts, theory, phenomena, and analysis techniques, such as Constant and product-cubic systems, Linear-univariate and product-cubic systems, Hyperbolic and hyperbolic-secant flows, Connected hyperbolic and hyperbolic-secant flows, Separated hyperbolic and hyperbolic-secant flows, Inflection-source (sink) Infinite-equilibriums and Infinite-equilibrium switching bifurcations. Develops a theory of product-cubic nonlinear systems with constant and single-variable linear vector fields; Presents inflection-source (sink) infinite-equilibriums for the switching of a connected hyperbolic flow; Presents inflection-sink (source) infinite-equilibriums for the switching of a paralleled hyperbolic flow. . Plasma waves. 69749 Multibody systems. 66046 Vibration. 66047 Mechanics, Applied. Dynamics. 65524 Nonlinear theories. 65525 Mathematics Data processing. 65715 Waves, instabilities and nonlinear plasma dynamics. 69750 Multibody Systems and Mechanical Vibrations. 66048 Applied Dynamical Systems. 65530 Engineering Mechanics. Computational Science and Engineering. 65717 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031570919 Printed edition: 9783031570933 Printed edition: 9783031570940 https://doi.org/10.1007/978-3-031-57092-6 ZDB-2-PHA ZDB-2-SXP 64659 64659