Luo

Two-dimensional Self and Product Cubic Systems, Vol. I

Self-linear and Crossing-quadratic Product Vector Field

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eBook. PDF

eBook

2024

232 S. X, 232 p. 43 illus., 42 illus. in color..

In englischer Sprache

Springer International Publishing. ISBN 978-3-031-57096-4

Produktbeschreibung

This book, the 14th of 15 related monographs on Cubic Dynamical Systems, discusses crossing and product cubic systems with a self-linear and crossing-quadratic product vector field. Dr. Luo discusses singular equilibrium series with inflection-source (sink) flows that are switched with parabola-source (sink) infinite-equilibriums. He further describes networks of simple equilibriums with connected hyperbolic flows are obtained, which are switched with inflection-source (sink) and parabola-saddle infinite-equilibriums, and nonlinear dynamics and singularity for such crossing and product cubic systems. In such cubic systems, the appearing bifurcations are:

  • double-inflection saddles,
  • inflection-source (sink) flows,
  • parabola-saddles (saddle-center),
  • third-order parabola-saddles,
  • third-order saddles (centers),
  • third-order saddle-source (sink).

  • Develops a theory of crossing and product cubic systems with a self-linear and crossing-quadratic product vector field;
  • Presents singular equilibrium series with inflection-source (sink) flows and networks of simple equilibriums;
  • Shows equilibrium appearing bifurcations of (2,2)-double-inflection saddles and inflection-source (sink) flows.

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