Introduction

This book examines infinite-equilibriums for the switching bifurcations of two 1-dimensional flows in dynamical systems. Quadratic single-linear-bivariate systems are adopted to discuss infinite-equilibriums in dynamical systems.

Types of Infinite-Equilibriums

For such quadratic dynamical systems, there are three types of infinite-equilibriums. The inflection-source and sink infinite-equilibriums are for the switching bifurcations of two parabola flows on the two directions. The parabola-source and sink infinite-equilibriums are for the switching bifurcations of parabola and inflection flows on the two directions. The inflection upper and lower-saddle infinite-equilibriums are for the switching bifurcation of two inflection flows in two directions.

Flow Dynamics

The inflection flows are for appearing bifurcations of two parabola flows on the same direction. Such switching bifurcations for 1-dimensional flow are based on the infinite-equilibriums, which will help one understand global dynamics in nonlinear dynamical systems.

Purpose of the Book

This book introduces infinite-equilibrium concepts and such switching bifurcations to nonlinear dynamics.