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.

Prof. Albert C. J. Luo is a distinguished research professor at the Department of Mechanical Engineering at Southern Illinois University Edwardsville, USA. He received his Ph.D. degree from the University of Manitoba, Canada, in 1995. His research focuses on nonlinear dynamics, nonlinear mechanics and nonlinear differential equations, and he has published over 60 monographs, 20 edited books, and more than 400 journal articles and conference papers in these fields. He received the Paul Simon Outstanding Scholar Award in 2008 and an ASME fellowship in 2007. He was an editor for Communications in Nonlinear Science and Numerical Simulation for 14 years, and an associate editor for ASME Journal of Computational and Nonlinear Dynamics, and International Journal of Bifurcation and Chaos. He now serves as a co-editor of the Journal of Applied Nonlinear Dynamics and editor of various book series, including “Nonlinear Systems and Complexity” and “Nonlinear Physical Science.”