Two-Dimensional Quadratic Nonlinear Systems

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 systemsIn 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 theoryHe 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 Dynamical Systems.- Chapter 2 Single-variable Quadratic Systems with a Self-univariate Quadratic Vector Field.- Chapter 3 Single-variable Quadratic Systems with a Non-self-univariate Quadratic Vector Field.- Chapter 4 Variable-independent quadratic systems.- Chapter 5 Variable-crossing univariate quadratic systems.- Chapter 6 Two-univariate product quadratic systems.- Chapter 7 Product-bivariate Quadratic Systems with Self-univariate Vector Fields.- Chapter 8 Product-bivariate Quadratic Systems with Non-self-univariate Vector Fields.