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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.