Applied Mathematics seminar | Albert C.J. Luo, Analytical Periodic Motions to Chaos in Nonlinear Dynamical Systems

MC 6460

Speaker

Albert C.J. Luo
Department of Mechanical and Industrial Engineering, Southern Illinois University at Edwardsville, USA

Title

Analytical Periodic Motions to Chaos in Nonlineral Dynamical Systems

Abstract

In this talk, analytical solutions for period-m flows and chaos in nonlinear dynamical systems will be presented through the generalized harmonic balance method. The nonlinear damping, periodically forced, quadratic nonlinear oscillator are studied as an example to demonstrate the analytical solutions of periodic motions and chaos. Through this investigation, the mechanism for a period-m motion jumping to another period-m motion in numerical computation is found. In this problem, the Hopf bifurcation of periodic motions is equivalent to the period-doubling bifurcation via Poincare mappings of dynamical systems. The stable and unstable period-m motions can be obtained analytically. Even more, the stable and unstable chaotic motions can be achieved analytically. The methodology presented in this paper can be applied to other nonlinear vibration systems, which is independent of small parameters.

Professor Luo has worked at Southern Illinois University Edwardsville. For over 30 years, Dr. Luo’s contributions on nonlinear dynamical systems and mechanics lie in (i) the local singularity theory for discontinuous dynamical systems, (ii) Dynamical systems synchronization, (iii) Analytical solutions of periodic and chaotic motions in nonlinear dynamical systems, (iv) The theory for stochastic and resonant layer in nonlinear Hamiltonian systems, (v) The full nonlinear theory for a deformable body. Such contributions have been scattered into 19 monographs and over 300 peer-reviewed journal and conference papers. Dr. Luo served editors for the Journal “Communications in Nonlinear Science and Numerical simulation”, book series on Nonlinear Physical Science (HEP) and Nonlinear Systems and Complexity (Springer). Dr. Luo is the editorial member for two journals (i.e., IMeCh E Part K Journal of Multibody Dynamics and Journal of Vibration and Control). He also organized over 30 international symposiums and conferences on Dynamics and Control.