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

Professor Albert C. J. Luo is currently a Distinguished Research Professor at Southern Illinois University Edwardsville (SIUE), USA, and an internationally renowned expert in the field of nonlinear dynamical systems theory and applications. Over the past 30 years, Professor Luo has made seminal contributions to theoretical physics, nonlinear dynamics, and applied mathematics. The novel "toolbox" and "way of thinking" he developed have significantly advanced the understanding of the deep-seated principles governing nonlinear, discontinuous, and complex systems. These contributions include: the theory of planar polynomial dynamical systems and solutions to Hilbert’s 16th problem; stability and bifurcation theory for nonlinear continuous dynamical systems; stability and bifurcation theory for nonlinear discrete dynamical systems; bifurcation dynamics; discontinuous dynamical system theory; generalized synchronization theory for dynamical systems; analytical and semi-analytical methods for periodic and chaotic motions in nonlinear dynamical systems; stochastic layer and resonance layer theory in nonlinear Hamiltonian systems; and dynamics of nonlinear deformable bodies. Professor Luo has published more than 400 peer-reviewed papers in prestigious journals and conference proceedings. He is the author of over 60 monographs and editor of more than 20 volumes. He serves as the editor-in-chief for the series Nonlinear Physical Science (co-published by Higher Education Press and Springer), the series Nonlinear Systems and Complexity (Springer), and the series Chaos, Nonlinearity, and Complexity (World Scientific). He is currently an associate editor for the International Journal of Bifurcation and Chaos and an editorial board member for the AIP journal Chaos.