Internal motion of the complex oscillators near main resonance

An analytical study of the two degrees of freedom nonlinear dynamical system is presented. The internal motion of the system is separated and described by one fourth order differential equation. An approximate approach allows reducing the problem to the Duffing equation with adequate initial conditions. A novel idea for an effective study of nonlinear dynamical systems consisting in a concept of the socalled limiting phase trajectories is applied. Both qualitative and quantitative complex analyses have been performed. Important nonlinear dynamical transition type phenomena are detected and discussed. In particular, nonsteady forced system vibrations are investigated analytically.