Self-Linear and Product-Cubic Systems

In this chapter, nonlinear dynamics and singularity of a self-linear and product cubic systems are discussed. For a self-linear and crossing-quadratic product, the inflection source and sink flows are the appearing bifurcation of the connected hyperbolic and hyperbolic-secant flows. The parabola-sink and parabola-source infinite-equilibriums are the switching bifurcation for inflection-sink and inflection-source flows with sink, source, and saddle. The series of hyperbolic and hyperbolic-secant flows with source, sink, and saddle are developed. For a self-crossing and self-quadratic product, the hyperbolic-to-hyperbolic-secant flows are the appearing bifurcations for the separated hyperbolic and hyperbolic-secant flows, and the saddle-source (sink) are the appearing bifurcations of the saddle and source (sink). The increasing-inflection source (sink) infinite-equilibriums are the switching bifurcations of saddle-source (sink) and hyperbolic-to-hyperbolic-secant flow with hyperbolic-secant-to-hyperbolic flows and saddle-source (sink). The matrix network of paralleled hyperbolic and hyperbolic-secant flows with source, sink, and saddle are developed. The inflection-sink and inflection-source infinite-equilibriums are the switching bifurcations of hyperbolic flow and saddle with the hyperbolic-secant flow and sink (source).