A limit cycle in a non-conservative sytem in 1:2 resonance

Systems with two degrees of freedom under the action of non-conservative forces and small linear viscous friction forces with complete dissipation are considered. A limit cycle that exists under specific conditions in the vicinity of an isolated equilibrium of the system is constructed using asymptotic methods in the case of 1:2 resonance. A criterion for asymptotic stability of this cycle is obtained to within equality-type relations. An estimate of the region of attraction of the limit cycle in a truncated system is given. Oscillations of a two-link rod system on a plane in 1:2 resonance are investigated. ©2011