| ISBN13: | 9783031570957 |
| ISBN10: | 3031570952 |
| Kötéstípus: | Keménykötés |
| Terjedelem: | 232 oldal |
| Méret: | 235x155 mm |
| Nyelv: | angol |
| Illusztrációk: | 1 Illustrations, black & white; 42 Illustrations, color |
| 671 |
Two-dimensional Self and Product Cubic Systems, Vol. I
EUR 171.19
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Back cover Materials
Albert C J Luo
Two-dimensional Self and Product Cubic Systems, Vol. I
Self-linear and crossing-quadratic product vector field
This book is the twelfth of 15 related monographs on Cubic Systems, discusses self and product cubic systems with a self-linear and crossing-quadratic product vector field. Equilibrium series with flow singularity are presented and the corresponding switching bifurcations are discussed. The volume explains how the equilibrium series with connected hyperbolic and hyperbolic-secant flows exist in such cubic systems, and that the corresponding switching bifurcations are obtained through the inflection-source and sink infinite-equilibriums. Finally, the author illustrates how, in such cubic systems, the appearing bifurcations include saddle-source (sink) for equilibriums and inflection-source and sink flows for the connected hyperbolic flows, and the third-order saddle, sink and source are the appearing and switching bifurcations for saddle-source (sink) with saddles, source and sink, and also for saddle, sink and source.
· Develops a theory of self and product cubic systems with a self-linear and crossing-quadratic product vector field;
· Presents equilibrium series with flow singularity and connected hyperbolic and hyperbolic-secant flows;
· Shows equilibrium series switching bifurcations through a range of sources and saddles on the infinite-equilibriums.
This book, the 14th of 15 related monographs on Cubic Dynamical Systems, discusses crossing and product cubic systems with a self-linear and crossing-quadratic product vector field. Dr. Luo discusses singular equilibrium series with inflection-source (sink) flows that are switched with parabola-source (sink) infinite-equilibriums. He further describes networks of simple equilibriums with connected hyperbolic flows are obtained, which are switched with inflection-source (sink) and parabola-saddle infinite-equilibriums, and nonlinear dynamics and singularity for such crossing and product cubic systems. In such cubic systems, the appearing bifurcations are:
- double-inflection saddles,
- inflection-source (sink) flows,
- parabola-saddles (saddle-center),
- third-order parabola-saddles,
- third-order saddles (centers),
- third-order saddle-source (sink).
Crossing and Product cubic Systems.- Double-inflection Saddles and Parabola-saddles.- Three Parabola-saddle Series and Switching Dynamics.- Parabola-saddles, (1:1) and (1:3)-Saddles and Centers.- Equilibrium Networks and Switching with Hyperbolic Flows.
