03455nam a22005535i 4500 978-3-031-48472-8 DE-He213 20251030113252.0 cr nn 008mamaa 241031s2024 sz | s |||| 0|eng d 9783031484728 978-3-031-48472-8 10.1007/978-3-031-48472-8 doi TA329-348 TBJ bicssc MAT003000 bisacsh TBJ thema Luo, Albert C. J. author. aut http://id.loc.gov/vocabulary/relators/aut 81241 Two-dimensional Single-Variable Cubic Nonlinear Systems, Vol. I [electronic resource] : A Self-univariate Cubic Vector Field / by Albert C. J. Luo. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. IX, 437 p. 32 illus., 31 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Chapter 1 Constant and Self-cubic Vector fields -- Chapter 2 Crossing-linear and Self-cubic Vector Fields -- Chapter 3 Crossing-quadratic and Self-Cubic Vector Fields -- Chapter 4 Two Single-variable Cubic Vector Fields. This book, the first of 15 related monographs, presents systematically a theory of cubic nonlinear systems with single-variable vector fields. The cubic vector fields are of self-variables and are discussed as the first part of the book. 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-dimensional cubic systems are for the first time to be presented. Third-order source and sink flows are presented, and the third-order parabola flows are also presented. The infinite-equilibriums are the switching bifurcations for the first and third-order source and sink flows, and the second-order saddle flows with the first and third-order parabola flows, and the inflection flows. The appearing bifurcations in such cubic systems includes saddle flows and third-order source (sink) flows, inflection flows and third-order up (down)-parabola flows. Develops the theory for 1-dimensonal flow singularity and bifurcations to elucidate dynamics of nonlinear systems; Provides a new research direction in nonlinear dynamics community; Shows how singularity and bifurcations occur not only for equilibriums and attractors but also for 1-dimensional flows. Engineering mathematics. 64145 Mechanics, Applied. Dynamics. 65524 Nonlinear theories. 65525 System theory. 66519 Engineering Mathematics. 64145 Engineering Mechanics. Applied Dynamical Systems. 65530 Complex Systems. 66520 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031484711 Printed edition: 9783031484735 Printed edition: 9783031484742 https://doi.org/10.1007/978-3-031-48472-8 ZDB-2-ENG ZDB-2-SXE 64611 64611