Luo A.C.J. Two-dimensional Product Cubic Systems, Vol. VII: Self- Quadratic Vector Field

Springer, 2024. — 240 p.This book is the seventh of 15 related monographs, concerns nonlinear dynamics and singularity of cubic dynamical systems possessing a product-cubic vector field and a self-univariate quadratic vector field. The equilibrium singularity and bifurcation dynamics are discussed. The saddle-source (sink) is the appearing bifurcations for saddle and source (sink). The double-saddle equilibriums are the appearing bifurcations of the saddle-source and saddle-sink, and also the appearing bifurcations of the network of saddles, sink and source. The infinite-equilibriums for the switching bifurcations include:
inflection-saddle infinite-equilibriums,
hyperbolic-source (sink) infinite-equilibriums,
up-down (down-up) saddle infinite-equilibriums,
inflection-source (sink) infinite-equilibriums.Preface
Self-Quadratic and Product-Cubic Systems
Self-Linear and Crossing-Quadratic Product Vector Fields
Proof of Theorem 1.1
Crossing-Linear and Self-Quadratic Product Vector Fields
Proof of Theorem 1.2
Saddle-Node Singularity and Bifurcation Dynamics
Cubic Systems with Crossing and Self-Singularities
Inflection-Source (Sink) Flows and Saddle-Source (Sink)
Inflection-Saddle Infinite-Equilibriums
Single Crossing-Singular Cubic Systems
Inflection-Source (Sink) Flows with Saddles, Source and Sink
Parabola-Source (Sink) Infinite-Equilibriums
Single Self-Singularity Cubic Systems
Saddle-Source (Sink) with Connected Hyperbolic Flows
Up-Down-to-Down-Up Upper-Saddles (Lower-Saddles)
Nonsingular Cubic Systems
Equilibrium Series with Connected Hyperbolic Flows
Inflection-Source (Sink) Switching Bifurcations
Double-Saddles and Switching Bifurcations
Double Self-Singular Cubic Systems
Double-Saddles with Hyperbolic-to-Hyperbolic-Secant Flows
Up-Down and Down-Up Upper-Saddles (Lower-Saddles)
Self-Singularity on the Product-Cubic Vector Fields
Saddle-Nodes with Hyperbolic to Hyperbolic-Secant Flows
Inflection-Source (Sink) Infinite-Equilibriums
Single Self-Singularity in the Self-Quadratic Vector Field
Saddle-Nodes with Paralleled Hyperbolic Flows
Up-Down-to-Down-Up Upper-Saddles (Lower-Saddles)
Nonsingular Cubic Systems
Equilibrium Networks with Paralleled Hyperbolic Flows
Connected Inflection-Sources (Sinks)
Index