Two-Univariate Product Quadratic Systems

Abstract

In this chapter, nonlinear dynamics of dynamical systems possessing bivariate quadratic vector fields is discussed as in Luo (Journal of Vibration Testing and System Dynamics in 2023). The bivariate quadratic vector field is a product of two different-variable univariate functions in two directions. The dynamical systems with two crossing-variable product bivariate vector fields are presented, and the corresponding global dynamics of such dynamical systems is presented. The hyperbolic and hyperbolic-secant flows with directrix flows are discussed. From the infinite-equilibriums, the inflection sink (or source) bifurcation is presented for the switching of hyperbolic flow and saddles with hyperbolic-secant flow and sink (or source). Parabola-saddle bifurcations are for the switching of saddle and hyperbolic-secant flow center and hyperbolic flow, which is called the saddle-center switching bifurcation. Inflection-diagonal saddle bifurcations are for the switching of the network of saddle and sink (or saddle and source) with hyperbolic and hyperbolic-secant flows.