Complex-plane approach for the analysis of an externally excited system with autoparametric resonance

An autoparametric system with external excitation was examined by Nabergoj R, Tondl A, and Virag Z. (Chaos, Solitons & Fractals 1994;4:263–273). For investigating the semi-trivial and the nontrivial solution, a different approach in terms of complex-plane variables is here presented. It is proved that autoparametric resonance is initiated when semi-trivial solution becomes unstable. The trajectory of the system transforms from a straight line to an elliptic path. Within a certain interval of the excitation frequency, chaotic motion becomes possible.