Local Dynamics of Planar Nonlinear Systems, Vol II

Single-Product Function Vector Fields
Erscheinungsjahr 2026
ISBN: 978-3-032-30010-2
Verlag: Springer Nature Switzerland AG

Buch, Englisch, 326 Seiten, Format (B × H): 155 mm x 235 mm

This second of three related books examines local dynamics of planar nonlinear systems with single product-function vector fields through polynomialization. The self or crossing-univariate function and single product function constitute function vector fields. Local hybrid arrays of 1-dimensional flows and local hybrid networks of equilibriums and 1-dimensinal in planar nonlinear dynamical systems are discussed. The 1-dimensional flows and equilibriums with infinite-equilibriums in planar nonlinear dynamical systems are discussed, and the switching bifurcations of two local hybrid networks of equilibriums and 1-dimensional flows are presented. For self-univariate and single product function vector fields, the self-univariate equilibriums are sink, source, saddle, saddle-sink and saddle-source, and double-saddles, and the corresponding hybrid networks are formed by self-univariate equilibriums and singular hyperbolic flows. For crossing-univariate and product function vector fields, the equilibriums are saddles and centers, parabola-saddles, and inflection-saddles. The local singular networks are formed by crossing-univariate equilibriums and singular/simple hyperbolic flows.

Zielgruppe

Research

Autoren/Hrsg.

Luo, Albert C. J.

Fachgebiete

• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Kybernetik, Systemtheorie, Komplexe Systeme
• Mathematik | Informatik EDV | Informatik Informatik Künstliche Intelligenz
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure

Inhaltsverzeichnis

Chapter 1 Constant and Porduct-fucntion Systems.- Chapter 2 Self and Product-Function Systems.- Chapter 3 Proof of Theorem 2.1.- Chapter 4 Crossing and Product-Function Systems.- Chapter 5 Proof of Theorem 4.1.- index.

Über Autor(innen)

Professor Albert C. J. Luo is currently a Distinguished Research Professor at Southern Illinois University Edwardsville (SIUE), USA, and an internationally renowned expert in the field of nonlinear dynamical systems theory and applications. Over the past 30 years, Professor Luo has made seminal contributions to theoretical physics, nonlinear dynamics, and applied mathematics. The novel "toolbox" and "way of thinking" he developed have significantly advanced the understanding of the deep-seated principles governing nonlinear, discontinuous, and complex systems. These contributions include: the theory of planar polynomial dynamical systems and solutions to Hilbert’s 16th problem; stability and bifurcation theory for nonlinear continuous dynamical systems; stability and bifurcation theory for nonlinear discrete dynamical systems; bifurcation dynamics; discontinuous dynamical system theory; generalized synchronization theory for dynamical systems; analytical and semi-analytical methods for periodic and chaotic motions in nonlinear dynamical systems; stochastic layer and resonance layer theory in nonlinear Hamiltonian systems; and dynamics of nonlinear deformable bodies. Professor Luo has published more than 400 peer-reviewed papers in prestigious journals and conference proceedings. He is the author of over 60 monographs and editor of more than 20 volumes. He serves as the editor-in-chief for the series Nonlinear Physical Science (co-published by Higher Education Press and Springer), the series Nonlinear Systems and Complexity (Springer), and the series Chaos, Nonlinearity, and Complexity (World Scientific). He is currently an associate editor for the International Journal of Bifurcation and Chaos and an editorial board member for the AIP journal Chaos.