04078nam a22006255i 4500 978-3-031-57108-4 DE-He213 20251030113319.0 cr nn 008mamaa 241120s2024 sz | s |||| 0|eng d 9783031571084 978-3-031-57108-4 10.1007/978-3-031-57108-4 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 Single-Variable Cubic Nonlinear Systems, Vol II [electronic resource] : A Crossing-variable Cubic Vector Field / by Albert C. J. Luo. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. IX, 240 p. 44 illus., 40 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda 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. 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. . Dynamics. 65524 Nonlinear theories. 65525 Engineering mathematics. 64145 Engineering Data processing. Functions of complex variables. 72222 Dynamical systems. Plasma waves. 69749 Applied Dynamical Systems. 65530 Mathematical and Computational Engineering Applications. Several Complex Variables and Analytic Spaces. 72225 Dynamical Systems. Waves, instabilities and nonlinear plasma dynamics. 69750 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031571077 Printed edition: 9783031571091 Printed edition: 9783031571107 https://doi.org/10.1007/978-3-031-57108-4 ZDB-2-ENG ZDB-2-SXE 65068 65068