Two-dimensional Two-product Cubic Systems, Vol I: Different Product Structure Vector Fields

by Albert C. J. Luo

Overview

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.

Product Details

ISBN-13:	9783031484865
Publisher:	Springer Nature Switzerland
Publication date:	11/06/2024
Edition description:	2024
Pages:	336
Product dimensions:	6.10(w) x 9.25(h) x (d)

About the Author

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.

Table of Contents

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.