【Lecture】Towards Infinite Bifurcation Trees of Period-1 Motions to Chaos in a Time-delayed, Twin-well Duffing Oscillator

Theme: Towards Infinite Bifurcation Trees of Period-1 Motions to Chaos in a Time-delayed, Twin-well Duffing Oscillator

Time: Wednesday, December 20, 2017  9:30-10:30 am

Location: RM A229, Aerospace Building

Lecturer: Albert C. J. Luo

Distinguished Research Professor, Department of Mechanical and Industrial Engineering, Southern Illinois University Edwardsville;

Visiting Professor, School of Aeronautics and Astronautics, Shanghai Jiao Tong University.
Bio:

Albert C. J. Luo is a distinguished research professor in Department of Mechanical and Industrial Engineering, Southern Illinois University Edwardsville. He completed his BS degree in Mechanical Engineering, Sichuan Institute of Chemical Technology, Zigong, Sichuan, China, 1984. He got his M.S. degree in Engineering Mechanics, Dalian University of Technology in 1990; He obtained his Ph.D. degree in Mechanical Engineering, University of Manitoba, Winnipeg, Manitoba, 1995. His Research Interests includes Discontinuous discrete dynamical systems, Periodic flows to chaos in time-delayed nonlinear systems, Bifurcation trees of periodic flows to chaos in nonlinear systems, synchronization of dynamical systems, Accelerated fatigue and damage evaluation of structures and machines, Thermally induced, nonlinear vibration of rotating machines, Nonlinear dynamics of micromechanical resonators, so and so forth, Prof. LUO Published 15 Monographs, edited 5 Books, and 13 Proceedings and 6 Special Issues for International Journals. He published 150+ Journal papers and presented 180+ conference papers. :He is co-editor for Journal of Applied Nonlinear Dynamics ( L&H Scientific). Associate editor for the journal Discontinuity, Nonlinearity and Complexity ( L&H Scientific) , Editor for book series on “Nonlinear Systems and Complexity” (Springer).

Abstract:

In this paper, bifurcation trees of periodic motions to chaos in a periodically forced, time-delayed, twin-well Duffing oscillator are predicted by a semi-analytical method. The twin-well Duffing oscillator is extensively used in physics and engineering. The bifurcation trees of periodic motions to chaos in nonlinear dynamical systems is very significant for determine motion complexity. Thus, the bifurcation trees for periodic motions to chaos in such a time-delayed, twin-well Duffing oscillator are obtained analytically. From the finite discrete Fourier series, harmonic frequency-amplitude characteristics for period-1 to period-4 motions are analyzed. The stability and bifurcation behaviors of the time-delayed Duffing oscillator are different from the non-time-delayed Duffing oscillator. From the analytical prediction, numerical illustrations of periodic motions in the time-delayed, twin-well Duffing oscillator are completed. The complexity of period-1 motions to chaos in nonlinear dynamical systems are strongly dependent on the distributions and quantity levels of harmonic amplitudes. As a slowly varying excitation becomes very slow, the excitation amplitude will approach infinity for the infinite bifurcation trees of period-1 motion to chaos. Thus infinite bifurcation trees of period-1 motion to chaos can be obtained.