TY  - BOOK
AU  - Luo,Albert C.J.
ED  - SpringerLink (Online service)
TI  - Two-dimensional Single-Variable Cubic Nonlinear Systems, Vol II: A Crossing-variable Cubic Vector Field 
SN  - 9783031571084
AV  - TA352-356 
U1  - 515.39 23
PY  - 2024///
CY  - Cham
PB  - Springer Nature Switzerland, Imprint: Springer
KW  - Dynamics
KW  - Nonlinear theories
KW  - Engineering mathematics
KW  - Engineering
KW  - Data processing
KW  - Functions of complex variables
KW  - Dynamical systems
KW  - Plasma waves
KW  - Applied Dynamical Systems
KW  - Mathematical and Computational Engineering Applications
KW  - Several Complex Variables and Analytic Spaces
KW  - Dynamical Systems
KW  - Waves, instabilities and nonlinear plasma dynamics
N1  - Constant and Self-Cubic Vector fields -- Self-linear and Self-cubic vector fields -- Self-quadratic and self-cubic vector fields  -- Two self-cubic vector fields
N2  - This book, the second of 15 related monographs, presents systematically a theory of cubic nonlinear systems with single-variable vector fields. The cubic vector fields are of crossing-variables, which are discussed as the second part. The 1-dimensional flow singularity and bifurcations are discussed in such cubic systems. The appearing and switching bifurcations of the 1-dimensional flows in such 2-diemnsional cubic systems are for the first time to be presented. Third-order parabola flows are presented, and the upper and lower saddle flows are also presented. The infinite-equilibriums are the switching bifurcations for the first and third-order parabola flows, and inflection flows with the first source and sink flows, and the upper and lower-saddle flows. The appearing bifurcations in such cubic systems includes inflection flows and third-order parabola flows, upper and lower-saddle flows. 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 Presents saddle flows plus third-order parabola flows and inflection flows as appearing flow bifurcations; Presents saddle flows plus third-order parabola flows and inflection flows as appearing flow bifurcations; Explains infinite-equilibriums for the switching of the first-order sink and source flows.
UR  - http://libcon.rec.uabc.mx:2048/login?url=https://doi.org/10.1007/978-3-031-57108-4
ER  -