Exact solutions for coupled Duffing oscillators

Abstract The exact analytical solution of a system made of two coupled Duffing oscillators is obtained. The mathematical solution is illustrated by means of some examples aimed at showing the dynamical phenomena occurring in the considered system. Frequency response curves are reported for different value of the parameters, highlighting the effects of the linear and nonlinear coupling between the two variables. The presence of various solution branches, up to four coexisting attractors, is reported.