Two-dimensional Crossing and Product Cubic Systems, Vol. II
Crossing-linear and Self-quadratic Product Vector Field
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Beschreibung
This book, the 15th of 15 related monographs on Cubic Dynamic Systems, discusses crossing and product cubic systems with a crossing-linear and self-quadratic product vector field. The author discusses series of singular equilibriums and hyperbolic-to-hyperbolic-scant flows that are switched through the hyperbolic upper-to-lower saddles and parabola-saddles and circular and hyperbolic upper-to-lower saddles infinite-equilibriums. Series of simple equilibrium and paralleled hyperbolic flows are also discussed, which are switched through inflection-source (sink) and parabola-saddle infinite-equilibriums. Nonlinear dynamics and singularity for such crossing and product cubic systems are presented. In such cubic systems, the appearing bifurcations are: parabola-saddles, hyperbolic-to-hyperbolic-secant flows, third-order saddles (centers) and parabola-saddles (saddle-center).
- Develops a theory of crossing and product cubic systems with a crossing-linear and self-quadratic product vector field;
- Presents equilibrium series with hyperbolic-to-hyperbolic-scant flows and with paralleled hyperbolic flows;
- Shows equilibrium series switching bifurcations by up-down hyperbolic upper-to-lower saddles, parabola-saddles, et al.
This book, the 15th of 15 related monographs on Cubic Dynamic Systems, discusses crossing and product cubic systems with a crossing-linear and self-quadratic product vector field. The author discusses series of singular equilibriums and hyperbolic-to-hyperbolic-scant flows that are switched through the hyperbolic upper-to-lower saddles and parabola-saddles and circular and hyperbolic upper-to-lower saddles infinite-equilibriums. Series of simple equilibrium and paralleled hyperbolic flows are also discussed, which are switched through inflection-source (sink) and parabola-saddle infinite-equilibriums. Nonlinear dynamics and singularity for such crossing and product cubic systems are presented. In such cubic systems, the appearing bifurcations are: parabola-saddles, hyperbolic-to-hyperbolic-secant flows, third-order saddles (centers) and parabola-saddles (saddle-center).
Develops a theory of crossing and product cubic systems with a crossing-linear and self-quadratic product vector field Presents equilibrium series with hyperbolic-to-hyperbolic-scant flows and with paralleled hyperbolic flows Shows equilibrium series switching bifurcations by up-down hyperbolic upper-to-lower saddles, parabola-saddles, et al
Autor*in
Albert C. J. Luo
Themen in »Two-dimensional Crossing and Product Cubic Systems, Vol. II«
Crossing and product cubic systems Self-linear and crossing-quadratic product vector field Crossing-cubic vector field Hybrid series of singular equilibriums and flows Double-inflection saddles appearing bifurcations Inflection-source (sink) flows appearing bifurcations Parabola-saddles (saddle-center) appearing bifurcations Third-order parabola-saddles appearing bifurcations Third-order saddles (centers) appearing bifurcations Third-order saddle-source (sink) appearing bifurcations parabola-source (sink) infinite-equilibriums parabola-saddle infinite-equilibriums inflection-source (sink) infinite-equilibrium