Bifurcations and chaos due to time delayed feedback in a non-autonomous system

摘要

A model studied in the paper is obtained by adding linear and nonlinear time delayed feedback of a representative non-autonomous system. The main attention is focused on the primary resonance when the excitation is at the same order as that of the nonlinear terms (including the time delay terms). The unstable regions for the limit cycles are also obtained, predicting the occurrence of chaotic motions. Numerical simulations are employed to examine the predictions.