Two-dimensional Two-product Cubic Systems, Vol I

Different Product Structure Vector Fields
2024
ISBN: 978-3-031-48486-5
Verlag: Springer Nature Switzerland

Buch, Englisch, 336 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 751 g

This book is the ninth of 15 related monographs, discusses a two product-cubic dynamical system possessing different product-cubic structures and the equilibrium and flow singularity and bifurcations for appearing and switching bifurcations. The appearing bifurcations herein are parabola-saddles, saddle-sources (sinks), hyperbolic-to-hyperbolic-secant flows, and inflection-source (sink) flows. The switching bifurcations for saddle-source (sink) with hyperbolic-to-hyperbolic-secant flows and parabola-saddles with inflection-source (sink) flows are based on the parabola-source (sink), parabola-saddles, inflection-saddles infinite-equilibriums. The switching bifurcations for the network of the simple equilibriums with hyperbolic flows are parabola-saddles and inflection-source (sink) on the inflection-source and sink infinite-equilibriums. Readers will learn new concepts, theory, phenomena, and analysis techniques.

· Two-different product-cubic systems

· Hybrid networks of higher-order equilibriums and flows

· Hybrid series of simple equilibriums and hyperbolic flows

· Higher-singular equilibrium appearing bifurcations

· Higher-order singular flow appearing bifurcations

· Parabola-source (sink) infinite-equilibriums

· Parabola-saddle infinite-equilibriums

· Inflection-saddle infinite-equilibriums

· Inflection-source (sink) infinite-equilibriums

· Infinite-equilibrium switching bifurcations.

Zielgruppe

Research

Autoren/Hrsg.

Luo, Albert C. J.

Fachgebiete

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

Inhaltsverzeichnis

Chapter 1 Cubic Systems with Two different Product Structures.- Chapter 2 Parabola-saddle and Saddle-source (sink) Singularity.-  Chapter 3 Inflection-source (sink) flows and parabola-saddles.- Chapter 4Saddle-source (sink) with hyperbolic flow singularity.- Chapter 5 Equilibrium matrices 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.