Overview

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.

Flow Types and Dynamics

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.

Bifurcations and Networks

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.

Illustrations and Understanding

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.