Two-dimensional Self and Product Cubic Systems, Vol. I

Self-linear and Crossing-quadratic Product Vector Field
2024
ISBN: 978-3-031-57095-7
Verlag: Springer Nature Switzerland

Buch, Englisch, 232 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 578 g

This book, the 14th of 15 related monographs on Cubic Dynamical Systems, discusses crossing and product cubic systems with a self-linear and crossing-quadratic product vector field. Dr. Luo discusses singular equilibrium series with inflection-source (sink) flows that are switched with parabola-source (sink) infinite-equilibriums. He further describes networks of simple equilibriums with connected hyperbolic flows are obtained, which are switched with inflection-source (sink) and parabola-saddle infinite-equilibriums, and nonlinear dynamics and singularity for such crossing and product cubic systems. In such cubic systems, the appearing bifurcations are:

•  double-inflection saddles, 
•  inflection-source (sink) flows,
•  parabola-saddles (saddle-center),
•  third-order parabola-saddles, 
•  third-order saddles (centers),
•  third-order saddle-source (sink).

Zielgruppe

Research

Autoren/Hrsg.

Luo, Albert C. J.

Fachgebiete

• Mathematik | Informatik EDV | Informatik Informatik Berechenbarkeitstheorie, Komplexitätstheorie
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Naturwissenschaften Physik Thermodynamik Plasmaphysik
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Statik, Dynamik, Kinetik, Kinematik
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie

Inhaltsverzeichnis

Crossing and Product cubic Systems.- Double-inflection Saddles and Parabola-saddles.- Three Parabola-saddle Series and Switching Dynamics.- Parabola-saddles, (1:1) and (1:3)-Saddles and Centers.- Equilibrium Networks and Switching with Hyperbolic Flows.

Über Autor(innen)

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.