Two-dimensional Single-Variable Cubic Nonlinear Systems, Vol II A Crossing-variable Cubic Vector Field / [electronic resource] :
by Albert C. J. Luo.
- 1st ed. 2024.
- IX, 240 p. 44 illus., 40 illus. in color. online resource.
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.
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 Presents saddle flows plus third-order parabola flows and inflection flows as appearing flow bifurcations; Presents saddle flows plus third-order parabola flows and inflection flows as appearing flow bifurcations; Explains infinite-equilibriums for the switching of the first-order sink and source flows. .