Two-dimensional Two-Product Polynomial Systems

This book is a six-volume handbook about two-product polynomial systems. The corresponding hybrid networks of singular and non-singular, 1-dimensional flows and equilibriums are presented. The higher-order singular 1-dimensional flows and singular equilibriums are for the appearing bifurcations of lower-order singular and non-singular 1-dimensional flows and equilibriums. The infinite-equilibriums are the switching bifurcations for two associated networks of singular and non-singular, 1-dimensional flows and equilibriums.     Volume I of this book presents a theorem for the bifurcation dynamics of two-product polynomial systems through a theorem. The nonlinear dynamics of  ingular flows and equilibriums with the corresponding infinite-equilibriums in two-product polynomial systems in theorem.     Volume II of this book presents the methodology to achieve the mathematical conditions for singular equilibriums, singular 1-dimensional flows, two network switching in the theorem through local analysis and the first integral manifolds.     Volume III of this book discusses the nonlinear dynamics of two-product polynomial systems with ([m1, 2n11+1], [m2, 2n21+1])-vector fields.     Volume IV of this book discusses the nonlinear dynamics of two-product polynomial systems with ([m1, 2n11], [m2, 2n21+1])-vector fields.     Volume V of this book discusses the nonlinear dynamics of two-product polynomial systems with ([m1, 2n11+1], [m2, 2n21])-vector fields.     Volume VI of this book discusses the nonlinear dynamics of two-product polynomial systems with ([m1, 2n11], [m2, 2n21])-vector fields. In volumes III-VI, the singular equilibriums and 1-dimensional flows in such two-product polynomial systems are presented first, and the singular infinite-equilibriums are presented for the switching bifurcations of two singular/simple hybrid networks of the two-product polynomial system.