Two-dimensional Single-Variable Cubic Nonlinear Systems, Vol II

Anglický jazyk

Two-dimensional Single-Variable Cubic Nonlinear Systems, Vol II

Vydavateľstvo: Springer Nature Switzerland
Rok vydania: 2024
Formát: Hardback
Rozmer: 241 x 160 mm
Jazyk: Anglický jazyk
ISBN: 9783031571077

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O knihe

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.