TY  - BOOK
AU  - Luo,Albert C.J.
ED  - SpringerLink (Online service)
TI  - Two-dimensional Product-Cubic Systems, Vol. I: Constant and Linear Vector Fields 
SN  - 9783031570926
AV  - QC718.5.W3 
PY  - 2024///
CY  - Cham
PB  - Springer Nature Switzerland, Imprint: Springer
KW  - Plasma waves
KW  - Multibody systems
KW  - Vibration
KW  - Mechanics, Applied
KW  - Dynamics
KW  - Nonlinear theories
KW  - Mathematics
KW  - Data processing
KW  - Waves, instabilities and nonlinear plasma dynamics
KW  - Multibody Systems and Mechanical Vibrations
KW  - Applied Dynamical Systems
KW  - Engineering Mechanics
KW  - Computational Science and Engineering
N1  - Constant and Product-Cubic Systems -- Self-linear and Product-cubic systems -- Crossing-linear and Product-cubic systems
N2  - 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.
UR  - https://doi.org/10.1007/978-3-031-57092-6
ER  -