Two-dimensional Single-Variable Cubic Nonlinear Systems, Vol II : A Crossing-variable Cubic Vector Field

Luo, Albert C. J.

Springer International Publishing AG（2025/11発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 240 p.
• 言語 ENG
• 商品コード 9783031571107

Full Description

This book, the second of 15 related monographs, presents systematically a theory of cubic nonlinear systems with single-variable vector fields. The cubic vector fields are of crossing-variables, which are discussed as the second part. The 1-dimensional flow singularity and bifurcations are discussed in such cubic systems. The appearing and switching bifurcations of the 1-dimensional flows in such 2-diemnsional cubic systems are for the first time to be presented. Third-order parabola flows are presented, and the upper and lower saddle flows are also presented. The infinite-equilibriums are the switching bifurcations for the first and third-order parabola flows, and inflection flows with the first source and sink flows, and the upper and lower-saddle flows.  The appearing bifurcations in such cubic systems includes inflection flows and third-order parabola flows, upper and lower-saddle flows. 

Readers will learn new concepts, theory, phenomena, and analytic techniques, including

Constant and crossing-cubic systems

Crossing-linear and crossing-cubic systems

Crossing-quadratic and crossing-cubic systems

Crossing-cubic and crossing-cubic systems

Appearing and switching bifurcations

Third-order centers and saddles

Parabola-saddles and inflection-saddles

Homoclinic-orbit network with centers

Appearing bifurcations

Contents

Constant and Self-Cubic Vector fields.- Self-linear and Self-cubic vector fields.- Self-quadratic and self-cubic vector fields .- Two self-cubic vector fields.