The book focuses on the nonlinear dynamics based on the vector fields with bivariate quadratic functions. This book is a unique monograph for two-dimensional quadratic nonlinear systems based on bivariate vector fields. Such a book provides different points of view about nonlinear dynamics and bifurcations of the quadratic dynamical systems on linear and nonlinear bivariate manifolds. Possible singular dynamics of the two-dimensional quadratic systems is discussed in detail. The dynamics of equilibriums and one-dimensional flows on bivariate manifolds are presented. Saddle-focus bifurcations are discussed, and switching bifurcations based on infinite-equilibriums are presented. Saddle-focus networks on bivariate manifolds are demonstrated. This book will serve as a reference book on dynamical systems and control for researchers, students and engineering in mathematics, mechanical and electrical engineering.

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 40 books and more than 350 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, and an associate editor for ASME Journal of Computational and Nonlinear Dynamics. He now serves as Co-editor of the Journal of Applied Nonlinear Dynamics and Editor of various book series, including Nonlinear Systems and Complexity and Nonlinear Physical Science.

His major contributions on nonlinear dynamical systems are:

             A theory for stochastic and resonant layers in nonlinear Hamiltonian systems

             A local theory and singularity for discontinuous dynamical systems

             Flow barriers theory for discontinuous dynamical systems

             Synchronization of continuous dynamical systems under specific constraints

             Synchronization and companion of discrete dynamical systems

             Analytical solutions of periodic motions in nonlinear systems

             Discretization and implicit mapping dynamics in nonlinear dynamical systems

             Periodic flows in time-delay systems

             Memorized nonlinear dynamical systems

In addition, Luo developed accurate theories for nonlinear deformable-body dynamics, machine tool dynamics and others:

             An approximate plate theory

             A theory for soft structures

             A nonlinear theory for beams and rods

             Fluid-induced nonlinear structural vibration

             A large damage theory for anisotropic materials

             A generalized fractal theory

He has published over 350 peer-reviewed journal and conference papers. Luo has been an editor for the Journal Communications in Nonlinear Science and Numerical simulation, and the book series on Nonlinear Systems and Complexity (Springer), and Nonlinear Physical Science (Higher Education Press and Springer).

Chapter 1 Two-dimensional Linear-bivariate Linear Systems.- Chapter 2 Single-linear-bivariate Quadratic Nonlinear Systems.- Chapter 3 Linear-bivariate Quadratic Dynamics.- Chapter 4 Linear-bivariate Product Quadratic Systems.- Chapter 5 Nonlinear-bivariate Quadratic Systems.