Two-dimensional Two-product Cubic Systems, Vol I : Different Product Structure Vector Fields / by Albert C. J. Luo.

Format:

Book

Author/Creator:

Luo, Albert C. J., author.

Language:

English

Subjects (All):

Dynamics.

Nonlinear theories.

Engineering mathematics.

Engineering--Data processing.

Engineering.

Multibody systems.

Vibration.

Mechanics, Applied.

Algebra, Universal.

Applied Dynamical Systems.

Mathematical and Computational Engineering Applications.

Multibody Systems and Mechanical Vibrations.

General Algebraic Systems.

Local Subjects:

Applied Dynamical Systems.

Mathematical and Computational Engineering Applications.

Multibody Systems and Mechanical Vibrations.

General Algebraic Systems.

Physical Description:

1 online resource (342 pages)

Edition:

1st ed. 2024.

Place of Publication:

Cham : Springer Nature Switzerland : Imprint: Springer, 2024.

Summary:

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.

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.

Notes:

Includes index.

ISBN:

9783031484872

3031484878