Two-dimensional Single-Variable Cubic Nonlinear Systems, Vol. I: A Self-univariate Cubic Vector Field

Luo, Albert C. J.

This book is the first of 15 related monographs, presents systematically a theory of cubic nonlinear systems with single-variable vector fields. The cubic vector fields are of self-variables and are discussed as the first part of the book. 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-dimensional cubic systems are for the first time to be presented. Third-order source and sink flows are presented, and the third-order parabola flows are also presented. The infinite-equilibriums are the switching bifurcations for the first and third-order source and sink flows, and the second-order saddle flows with the first and third-order parabola flows, and the inflection flows. The appearing bifurcations in such cubic systems includes saddle flows and third-order source (sink) flows, inflection flows and third-order up (down)-parabola flows.

Details

Published by: Springer

Publication Date: 2024-10-31

Format: Hardcover

ISBN-13: 9783031484711

DOI: 10.1007/978-3-031-48472-8

Dimensions: 235cm x155cm

Pages: 437