Bifurcation Trees of Period-m Motions to Chaos in a Time-Delayed, Quadratic Nonlinear Oscillator under a Periodic Excitation - Luo, Albert C. J.; Jin, Hanxiang (Discontinuity, Nonlinearity, and Complexity, 2026)
In this paper, analytical solutions of periodic motions in a periodi- cally excited, time-delayed, quadratic nonlinear oscillator are obtained through the Fourier series, and the stability and bifurcation of such pe- riodic motions are discussed by eigenvalue analysis. The analytical bifurcation tree of period-1 motion to chaos in such a time-delayed, quadratic oscillator is presented through period-1 to period-8 motion. Numerical illustrations of stable and unstable periodic motions are given by numerical and analytical solutions. Compared to dynami- cal systems without time-delay, the time-delayed dynamical systems possess different periodic motions and the bifurcation trees of periodic motions to chaos are also distinguishing.