Siyuan Xing

Time-Delay Effects on Periodic Motions in a Duffing Oscillator

In this chapter, time-delay effects on periodic motions in a periodically forced, time-delayed, hardening Duffing oscillator are reviewed and further discussed. Bifurcation trees of periodic motions to chaos varying with time-delay are presented for such a time-delayed, Duffing oscillator. From the analytical prediction, periodic motions in the time-delayed, hardening Duffing oscillator are simulated numerically. Through numerical illustrations, time-delay effects on period-1 motions to chaos in nonlinear dynamical systems are strongly related to the distributions and quantity levels of harmonic amplitudes.

Period-3 Motions in a Periodically Forced, Damped, Double-Well Duffing Oscillator With Time-Delay

In this paper, period-3 motions in a double-well Duffing oscillator with time-delay are predicted by a semi-analytical method. The implicit mapping structures of period-3 motions are constructed through the implicit mappings obtained by discretization of the corresponding differential equation. Complex period-3 motions are predicted through nonlinear algebraic equations of the implicit mappings in the mapping structures and the corresponding stability and bifurcation are carried out through eigenvalue analysis. Numerical and analytical results of complex period-3 motions are obtained and the corresponding frequency-amplitude characteristics are presented.Copyright

Bifurcation Trees of Period-1 Motions to Chaos in a Quadratic Nonlinear Oscillator With Time-Delayed Displacement

In this paper, periodic motions in a periodically forced, damped, quadratic nonlinear oscillator with time-delayed displacement are analytically predicted through implicit discrete mappings. The implicit discrete maps are obtained from discretization of differential equation of such a quadratic nonlinear oscillator. From mapping structures, bifurcation trees of periodic motions are achieved analytically, and the corresponding stability and bifurcation analysis are completed through eigenvalue analysis. From the analytical prediction, numerical results of periodic motions are illustrated to verify such an analytical prediction.Copyright