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2024 | Buch

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Two-dimensional Two-product Cubic Systems, Vol I

Different Product Structure Vector Fields

verfasst von: Albert C. J. Luo

Verlag: Springer Nature Switzerland

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik"

Inhaltsverzeichnis

Über dieses Buch

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.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Cubic Systems with Two Different Product Structure Vector Fields

In this chapter, nonlinear dynamics and singularity of cubic dynamical systems possessing two cubic vector fields of different product structures (i.e., self-linear and crossing-quadratic product and crossing-linear and self-quadratic product) are discussed

Albert C. J. Luo

Chapter 2. Parabola-Saddle and Saddle-Source (Sink) Singularity

Abstract

In this section, parabola saddles, saddle sources (sinks) singularities with the hyperbolic-to-hyperbolic secant flows and inflection source (sink) singularities in the two different product cubic systems are presented, and the corresponding bifurcation dynamics are discussed. The switching bifurcations of the parabola saddle with hyperbolic-to-hyperbolic secant flows and saddle source (sink) with inflection source (sink) flows are presented, and the switching bifurcations of saddle source (sink) with hyperbolic-to-hyperbolic secant flow and the parabola saddle with inflection source (sink) flow.

Albert C. J. Luo

Chapter 3. Inflection-Source (Sink) Flows and Parabola-Saddles

Abstract

In this chapter, inflection source (sink) flows and parabola saddles with hyperbolic flows and simple equilibriums are discussed, and the corresponding networks are presented for inflection flows and parabola saddles with simple flow and equilibriums. The corresponding switching bifurcations are discussed through the infinite equilibriums, which are parabola source (sink) infinite equilibriums, inflection source (sink) infinite equilibriums, and two infinite equilibriums of parabola source (sink) and inflection source (sink).

Albert C. J. Luo

Chapter 4. Saddle-Source (Sink) with Hyperbolic Flow Singularity

Abstract

In this chapter, saddle source (sink) flows and hyperbolic flow singularity with hyperbolic flows, positive or negative saddles, and center are discussed, and the corresponding networks are presented for saddle source (sink) and hyperbolic flow singularity with simple flow and equilibriums. The corresponding switching bifurcations are discussed through the infinite equilibrium, which includes up-down and down-up infinite equilibriums, inflection source (sink) infinite equilibriums, and two infinite equilibriums of inflection source (sink) and up-down (down-up) saddles.

Albert C. J. Luo

Chapter 5. Equilibrium Matrices with Hyperbolic Flows

Abstract

In this chapter, equilibrium matrices of saddle, center, saddle, source, and sink with hyperbolic flows are discussed, and the corresponding switching bifurcations are discussed. The inflection source (sink) infinite equilibriums exist in the vertical and horizontal directions. The parabola saddles are for a hyperbolic secant flow with a paralleled saddle and for a hyperbolic secant flow with a paralleled center. The inflection sources (sinks) are for a hyperbolic secant flow with a connected source (sink) and for a hyperbolic flow with a connected saddle.

Albert C. J. Luo

Backmatter

Titel: Two-dimensional Two-product Cubic Systems, Vol I
verfasst von: Albert C. J. Luo
Verlag: Springer Nature Switzerland
Electronic ISBN: 978-3-031-48487-2
Print ISBN: 978-3-031-48486-5
DOI: https://doi.org/10.1007/978-3-031-48487-2

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