This third of three related books examines local dynamics of planar nonlinear dynamical systems with two product-function vector fields through polynomialization. The equilibriums in two-product function systems include self-univariate and crossing-univariate equilibriums. The singular self and crossing-equilibriums and singular hyperbolic-flows are presented first, and the singular infinite-equilibriums are discussed for switching of self and crossing-equilibriums with hyperbolic flows. Local singular hybrid networks of self and crossing-equilibriums and hyperbolic flows in two-product function planar systems are discussed, and infinite-equilibriums in local singular hybrid networks are obtained. The simple 1-dimensional flows and equilibriums with infinite-equilibriums in two-product function systems are discussed, and the switching bifurcations of two local hybrid networks are presented
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