Two-dimensional Self and Product Cubic Systems, Vol. II
Crossing-linear and Self-quadratic Product Vector Field
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Beschreibung
This book is the thirteenth of 15 related monographs on Cubic Dynamical Systems, discusses self- and product-cubic systems with a crossing-linear and self-quadratic products vector field. Equilibrium series with flow singularity are presented and the corresponding switching bifurcations are discussed through up-down saddles, third-order concave-source (sink), and up-down-to-down-up saddles infinite-equilibriums. The author discusses how equilibrium networks with paralleled hyperbolic and hyperbolic-secant flows exist in such cubic systems, and the corresponding switching bifurcations obtained through the inflection-source and sink infinite-equilibriums. In such cubic systems, the appearing bifurcations are:
saddle-source (sink)
hyperbolic-to-hyperbolic-secant flows
double-saddle
third-order saddle, sink and source
third-order saddle-source (sink)
- Develops a theory of self and product cubic systems with a crossing-linear and self-quadratic products vector field;
- Presents equilibrium networks with paralleled hyperbolic and hyperbolic-secant flows with switching by up-down saddles;
- Shows equilibrium appearing bifurcations of various saddles, sinks, and flows.
This book is the thirteenth of 15 related monographs on Cubic Dynamical Systems, discusses self- and product-cubic systems with a crossing-linear and self-quadratic products vector field. Equilibrium series with flow singularity are presented and the corresponding switching bifurcations are discussed through up-down saddles, third-order concave-source (sink), and up-down-to-down-up saddles infinite-equilibriums. The author discusses how equilibrium networks with paralleled hyperbolic and hyperbolic-secant flows exist in such cubic systems, and the corresponding switching bifurcations obtained through the inflection-source and sink infinite-equilibriums. In such cubic systems, the appearing bifurcations are:
saddle-source (sink)
hyperbolic-to-hyperbolic-secant flows
double-saddle
third-order saddle, sink and source
third-order saddle-source (sink)
Develops a theory of self and product cubic systems with a crossing-linear and self-quadratic products vector field Presents equilibrium networks with paralleled hyperbolic and hyperbolic-secant flows with switching by up-down saddles Shows equilibrium appearing bifurcations of various saddles, sinks, and flows
Autor*in
Albert C. J. Luo
Themen in »Two-dimensional Self and Product Cubic Systems, Vol. II«
Self and product cubic systems Crossing-linear and self-quadratic product vector field Self-cubic vector field Hybrid networks of singular equilibriums and flows Hybrid networks of saddles, centers, and hyperbolic flows Saddle-source (sink) appearing bifurcations Hyperbolic-to-hyperbolic-secant flow appearing bifurcations Third-order saddle, source and sink appearing bifurcations Double-saddle appearing bifurcations Third-order saddle (sink or source) appearing bifurcations Third-order saddle-source (sink) appearing bifurcations up-down saddles infinite-equilibriums third-order concave-source (sink) infinite-equilibriums up-down-to-down-up saddle infinite-equilibriums inflection-source (sink) infinite-equilibrium