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

Crossing-linear and Self-quadratic Product Vector Field
2024
ISBN: 978-3-031-59573-8
Verlag: Springer Nature Switzerland

Buch, Englisch, 238 Seiten, HC runder Rücken kaschiert, Format (B × H): 160 mm x 241 mm, Gewicht: 586 g

This book is the thirteenth of 15 related monographs on Cubic Dynamical Systems, discusses self- and product-cubic systems with a crossing-linear and self-quadratic products vector field. Equilibrium series with flow singularity are presented and the corresponding switching bifurcations are discussed through up-down saddles, third-order concave-source (sink), and up-down-to-down-up saddles infinite-equilibriums. The author discusses how equilibrium networks with paralleled hyperbolic and hyperbolic-secant flows exist in such cubic systems, and the corresponding switching bifurcations obtained through the inflection-source and sink infinite-equilibriums. In such cubic systems, the appearing bifurcations are:

saddle-source (sink)

hyperbolic-to-hyperbolic-secant flows

double-saddle

third-order saddle, sink and source

third-order saddle-source (sink)

Zielgruppe

Research

Autoren/Hrsg.

Luo, Albert C. J.

Fachgebiete

• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Kontinuumsmechanik
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Kybernetik, Systemtheorie, Komplexe Systeme
• Mathematik | Informatik Mathematik Algebra

Inhaltsverzeichnis

Self and Product Cubic Systems.- Double-saddles, Third-order Saddle nodes.- Vertical Saddle-node Series and Switching Dynamics.- Saddle-nodes and third-order Saddles Source and Sink.- Simple equilibrium networks and switching dynamics.

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.