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Cubic Dynamical Systems, Vol. IX: Two-dimensional Two-product Cubic Systems with Different Product Structure Vector Fields de Albert C. J. Luo

Cubic Dynamical Systems, Vol. IX: Two-dimensional Two-product Cubic Systems with Different Product Structure Vector Fields

Autor Albert C. J. Luo
en Limba Engleză Hardback – 16 sep 2024
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.
 
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Specificații

ISBN-13: 9783031484865
ISBN-10: 303148486X
Pagini: 330
Ilustrații: Approx. 330 p. 45 illus. in color.
Dimensiuni: 155 x 235 mm
Ediția:2024
Editura: Springer Nature Switzerland
Colecția Springer
Locul publicării:Cham, Switzerland

Cuprins

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.

Notă biografică

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.

Textul de pe ultima copertă

This book, 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.
  • Develops a theory of nonlinear dynamics and singularity of two-different product-cubic dynamical systems;
  • Presents networks of singular and simple equilibriums and hyperbolic flows in such different structure product-cubic systems;
  • Reveals network switching bifurcations through infinite-equilibriums of parabola-source (sink) and parabola-saddles.


Caracteristici

Develops a theory of nonlinear dynamics and singularity of two-different product-cubic dynamical systems Presents networks of singular and simple equilibriums and hyperbolic flows Reveals network switching bifurcations through infinite-equilibriums of parabola