Response regimes of integrable damped strongly nonlinear oscillator under impact periodic forcing

We investigate the response regimes of integrable strongly nonlinear damped oscillator in the conditions of periodic impact loading. Integrability is achieved by special choice of the coefficients of the model. Stable and unstable response regimes corresponding to single-period responses are revealed analytically. Numeric simulations are undertaken in order to verify the extent to which the single-period solutions describe the global dynamics of the system. For some regions in the space of parameters and initial conditions it is the case; for others, co-existence of different response regimes for different initial conditions is revealed and investigated.