A system of self-excited, nonlinear differential equations exhibiting frequency entrainment is studied. Although similar equations describe electrical oscillators and machine-tool chattering, the results presented herein apply specifically to a model for the vortex-induced oscillation of linear structures. The equations are treated analytically by an approximate method, and two cases — partial nonlinear coupling and full nonlinear coupling — are identified. As applied to vortex-induced oscillations, the partially coupled case describes a structure having a single mode of oscillations, while the fully coupled case approximates continuous systems, such as undersea cables. Solutions for each case are examined for stability, and the results reveal several new types of behavior.

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