Chaotic Responses in a Stable Duffing System of Non-ideal Type

Abstract

In this paper the dynamics of a non-linear system with non-ideal excitation are studied. An unbalanced motor with a strong non-linear structure is considered. The excitation is of non-ideal type. The model is described with a system of two coupled strong non-linear differential equations. The steady state motions and their stability is studied applying the asymptotic methods. The existence of the Sommerfeld effect in such non-linear non-idealy excited system is proved. For certain values of system parameters chaotic motion appears. The chaos is realized through period doubling bifurcation. The results of numerical simulation are plotted and the Lyapunov exponents are calculated. The Pyragas method for control of chaotic motion is applied. The parameter values for transforming the chaos into periodical motion are obtained.