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

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