Two-dimensional Single-Variable Cubic Nonlinear Systems, Vol II - Luo, Albert C. J.

. .

Résumé :
This book, the second of 15 related monographs, presents systematically a theory of cubic nonlinear systems with single-variable vector fields. The cubic vector fields are of crossing-variables, which are discussed as the second part. The 1-dimensional flow singularity and bifurcations are discussed in such cubic systems. The appearing and switching bifurcations of the 1-dimensional flows in such 2-diemnsional cubic systems are for the first time to be presented. Third-order parabola flows are presented, and the upper and lower saddle flows are also presented. The infinite-equilibriums are the switching bifurcations for the first and third-order parabola flows, and inflection flows with the first source and sink flows, and the upper and lower-saddle flows. The appearing bifurcations in such cubic systems includes inflection flows and third-order parabola flows, upper and lower-saddle flows. Readers will learn new concepts, theory, phenomena, and analytic techniques, including Constant and crossing-cubic systems Crossing-linear and crossing-cubic systems Crossing-quadratic and crossing-cubic systems Crossing-cubic and crossing-cubic systems Appearing and switching bifurcations Third-order centers and saddles Parabola-saddles and inflection-saddles Homoclinic-orbit network with centers Appearing bifurcations...

Biographie:
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)....