Two-dimensional Self and Product Cubic Systems, Vol. I
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).
| Autor: | Luo, Albert C. J. |
|---|---|
| ISBN: | 9783031570957 |
| Sprache: | Englisch |
| Seitenzahl: | 232 |
| Produktart: | Gebunden |
| Verlag: | Springer International Publishing |
| Veröffentlicht: | 16.11.2024 |
| Untertitel: | Self-linear and Crossing-quadratic Product Vector Field |
| Schlagworte: | Crossing-cubic vector field Crossing and product cubic systems Double-inflection saddles appearing bifurcations Hybrid series of singular equilibriums and flows Inflection-source (sink) flows appearing bifurcations Parabola-saddles (saddle-center) appearing bifurcations Self-linear and crossing-quadratic product vector field Third-order parabola-saddles appearing bifurcations Third-order saddle-source (sink) appearing bifurcations Third-order saddles (centers) appearing bifurcations |
Dr. Albert C. J. Luo is a Distinguished Research Professor at the Southern Illinois University Edwardsville, in Edwardsville, IL, USA. Dr. Luo worked on Nonlinear Mechanics, Nonlinear Dynamics, and Applied Mathematics. He proposed and systematically developed: (i) the discontinuous dynamical system theory, (ii) analytical solutions for periodic motions in nonlinear dynamical systems, (iii) the theory of dynamical system synchronization, (iv) the accurate theory of nonlinear deformable-body dynamics, (v) new theories for stability and bifurcations of nonlinear dynamical systems. He discovered new phenomena in nonlinear dynamical systems. His methods and theories can help understanding and solving the Hilbert sixteenth problems and other nonlinear physics problems. The main results were scattered in 45 monographs in Springer, Wiley, Elsevier, and World Scientific, over 200 prestigious journal papers, and over 150 peer-reviewed conference papers.