报告题目： Towards infinite Bifurcation Trees in the time-delay Duffing Oscillator
报告人: Professor Albert C. J. Luo,
Department of Mechanical and Industrial Engineering, Southern Illinois University Edwardsville.
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 de-pendent 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.
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” for 14 years, 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 40 international symposiums and conferences on Dynamics and Control.