Two-dimensional Two-product Cubic Systems Vol.II - Luo, Albert C. J.
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This book is the tenth of 15 related monographs, discusses product-cubic nonlinear systems with two crossing-linear and self-quadratic products vector fields and the dynamic behaviors and singularity are presented through the first integral manifolds. The equilibrium and flow singularity and bifurcations discussed in this volume are for the appearing and switching bifurcations. The double-saddle equilibriums described are the appearing bifurcations for saddle source and saddle-sink, and for a network of saddles, sink and source. The infinite-equilibriums for the switching bifurcations are also…mehr

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Produktbeschreibung
This book is the tenth of 15 related monographs, discusses product-cubic nonlinear systems with two crossing-linear and self-quadratic products vector fields and the dynamic behaviors and singularity are presented through the first integral manifolds. The equilibrium and flow singularity and bifurcations discussed in this volume are for the appearing and switching bifurcations. The double-saddle equilibriums described are the appearing bifurcations for saddle source and saddle-sink, and for a network of saddles, sink and source. The infinite-equilibriums for the switching bifurcations are also presented, specifically:

· Inflection-saddle infinite-equilibriums,

· Hyperbolic (hyperbolic-secant)-sink and source infinite-equilibriums

· Up-down and down-up saddle infinite-equilibriums,

· Inflection-source (sink) infinite-equilibriums.

Autorenporträt
This book is a monograph about 1-dimensional flow arrays and bifurcations in constant and product polynomial systems. The 1-dimensional flows and the corresponding bifurcation dynamics are discussed. The singular hyperbolic and hyperbolic-secant flows are presented, and the singular hyperbolic-to-hyperbolic-secant flows are discussed. The singular inflection source, sink and upper, and lower-saddle flows are presented. The corresponding appearing and switching bifurcations are presented for the hyperbolic and hyperbolic-secant networks, and singular flows networks. The corresponding theorem is presented, and the proof of theorem is given. Based on the singular flows, the corresponding hyperbolic and hyperbolic-secant flows are illustrated for a better understanding of the dynamics of constant and product polynomial systems.