Local Dynamics of Planar Nonlinear Systems, Vol II
Single-Product Function Vector Fields
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Beschreibung
This second of three related books examines local dynamics of planar nonlinear systems with single product-function vector fields through polynomialization. The self or crossing-univariate function and single product function constitute function vector fields. Local hybrid arrays of 1-dimensional flows and local hybrid networks of equilibriums and 1-dimensinal in planar nonlinear dynamical systems are discussed. The 1-dimensional flows and equilibriums with infinite-equilibriums in planar nonlinear dynamical systems are discussed, and the switching bifurcations of two local hybrid networks of equilibriums and 1-dimensional flows are presented. For self-univariate and single product function vector fields, the self-univariate equilibriums are sink, source, saddle, saddle-sink and saddle-source, and double-saddles, and the corresponding hybrid networks are formed by self-univariate equilibriums and singular hyperbolic flows. For crossing-univariate and product function vector fields, the equilibriums are saddles and centers, parabola-saddles, and inflection-saddles. The local singular networks are formed by crossing-univariate equilibriums and singular/simple hyperbolic flows.
- Introduces polynomialization of nonlinear dynamical systems rather than Linearization
- Develops local dynamics of single-product function systems
- Advances bifurcation dynamics of single-product function systems
This second of three related books examines local dynamics of planar nonlinear systems with single product-function vector fields through polynomialization. The self or crossing-univariate function and single product function constitute function vector fields. Local hybrid arrays of 1-dimensional flows and local hybrid networks of equilibriums and 1-dimensinal in planar nonlinear dynamical systems are discussed. The 1-dimensional flows and equilibriums with infinite-equilibriums in planar nonlinear dynamical systems are discussed, and the switching bifurcations of two local hybrid networks of equilibriums and 1-dimensional flows are presented. For self-univariate and single product function vector fields, the self-univariate equilibriums are sink, source, saddle, saddle-sink and saddle-source, and double-saddles, and the corresponding hybrid networks are formed by self-univariate equilibriums and singular hyperbolic flows. For crossing-univariate and product function vector fields, the equilibriums are saddles and centers, parabola-saddles, and inflection-saddles. The local singular networks are formed by crossing-univariate equilibriums and singular/simple hyperbolic flows.
Introduces polynomialization of nonlinear dynamical systems rather than Linearization Develops local dynamics of single-product function systems Advances bifurcation dynamics of single-product function systems
Autor*in
Albert C. J. Luo
Themen in »Local Dynamics of Planar Nonlinear Systems, Vol II«
Constant and self-univariate function systems Constant and crossing-univariate function systems Single-variable function systems Self-univariate function systems Crossing-univariate function system Approximate polynomialized systems Singular self-flows Singular crossing-flows Singular self-flow arrays Singular crossing-flow arrays Local hybrid arrays of self and crossing flows Infinite-equilibriums for two hybrid flows arrays Singular self-equilibriums Singular crossing-equilibriums Bifurcation of singular self-equilibriums