In this chapter, dynamical systems possessing two quadratic vector fields with a single-linear-bivariate function will be discussed. Two inflection flows exist in such quadratic systems for appearing bifurcations of up- and down-parabola flows. The parabola source and sink infinite-equilibriums are for the switching bifurcations of parabola and inflection flows. The inflection source and sink infinite-equilibriums are for the switching bifurcations of two parabola flows in two directions. The inflection upper and lower-saddle infinite-equilibriums are for the switching bifurcations between two inflection flows in two directions. The corresponding parabola-flow arrays exist in such quadratic systems.

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Single-Linear-Bivariate Quadratic Systems

  • Albert C. J. Luo

摘要

In this chapter, dynamical systems possessing two quadratic vector fields with a single-linear-bivariate function will be discussed. Two inflection flows exist in such quadratic systems for appearing bifurcations of up- and down-parabola flows. The parabola source and sink infinite-equilibriums are for the switching bifurcations of parabola and inflection flows. The inflection source and sink infinite-equilibriums are for the switching bifurcations of two parabola flows in two directions. The inflection upper and lower-saddle infinite-equilibriums are for the switching bifurcations between two inflection flows in two directions. The corresponding parabola-flow arrays exist in such quadratic systems.