On frequency responses of period-1 motions to chaos in a periodically forced, time-delayed quadratic nonlinear system

Abstract

In this paper, frequency responses of periodic motions to chaos in a periodically forced, damped, quadratic nonlinear oscillator are investigated through the finite Fourier series analysis of discrete solutions of periodic motions. The discrete solutions of periodic motions are obtained from mapping structures of discrete nodes, and the corresponding stability and bifurcation analysis of periodic motions are completed by the eigenvalue analysis of fixed points in discrete nonlinear dynamical systems. The frequencyamplitude characteristics for bifurcation trees of periodic motions to chaos are discussed, and the quantity levels of harmonic amplitudes for different harmonic orders are illustrated clearly. Numerical results of periodic motions are illustrated to show harmonic frequency responses effects on periodic motions.