Two-dimensional Single-Variable Cubic Nonlinear Systems, Vol. I - Albert C. J. Luo

Two-dimensional Single-Variable Cubic Nonlinear Systems, Vol. I

A Self-univariate Cubic Vector Field
Buch | Hardcover
IX, 437 Seiten
2024
Springer International Publishing (Verlag)
978-3-031-48471-1 (ISBN)
192,59 inkl. MwSt

This book is 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.

Dr. Albert C. J. Luo is a Distinguished Research Professor at the Southern Illinois University Edwardsville, in Edwardsville, IL, USA. Dr. Luo worked on Nonlinear Mechanics, Nonlinear Dynamics, and Applied Mathematics. He proposed and systematically developed: (i) the discontinuous dynamical system theory, (ii) analytical solutions for periodic motions in nonlinear dynamical systems, (iii) the theory of dynamical system synchronization, (iv) the accurate theory of nonlinear deformable-body dynamics, (v) new theories for stability and bifurcations of nonlinear dynamical systems. He discovered new phenomena in nonlinear dynamical systems. His methods and theories can help understanding and solving the Hilbert sixteenth problems and other nonlinear physics problems. The main results were scattered in 45 monographs in Springer, Wiley, Elsevier, and World Scientific, over 200 prestigious journal papers, and over 150 peer-reviewed conference papers.

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.

Erscheinungsdatum
Zusatzinfo IX, 437 p. 32 illus., 31 illus. in color.
Verlagsort Cham
Sprache englisch
Maße 155 x 235 mm
Themenwelt Mathematik / Informatik Informatik Theorie / Studium
Mathematik / Informatik Mathematik Angewandte Mathematik
Technik Maschinenbau
Schlagworte appearing bifurcations • Constant and self-cubic systems • Crossing-linear and self-cubic systems • Crossing-quadratic and self-cubic systems • Infinite-equilibriums • Inflection sinks, sources and saddles • Logarithmic and concave sinks and sources • Parabola sinks, sources and saddles • switching bifurcations • Third-order parabola flows and inflection flows • Third-order sink and source flows and saddle flows • Two single-variable cubic systems • Up-down and down-up saddles
ISBN-10 3-031-48471-1 / 3031484711
ISBN-13 978-3-031-48471-1 / 9783031484711
Zustand Neuware
Haben Sie eine Frage zum Produkt?
Mehr entdecken
aus dem Bereich
Grundlagen – Anwendungen – Perspektiven

von Matthias Homeister

Buch | Softcover (2022)
Springer Vieweg (Verlag)
34,99
Eine Einführung in die Systemtheorie

von Margot Berghaus

Buch | Softcover (2022)
UTB (Verlag)
25,00