Ageing of an oscillator due to frequency switching

If an oscillator is driven by a force that switches between two frequencies, the dynamics it exhibits depends on precise manner of switching. Here we take one-dimensional and consider scenarios in which switching occurs: (i) driving forces have different or (ii) as single forcing whose frequency values. The difference subtle, but entirely changes long term behaviour, concerns whether switch can be expressed linearly nonlinearly terms discontinuous quantity (such sign Heaviside step function represents frequencies). In scenario has stable periodic orbit, system described Filippov system. hidden dynamics, lies outside theory Filippov's systems, causes to increasingly (as time passes) dominated sliding along frequency-switching threshold, particular if orbits do exist, they too exhibit sliding. We show behaviour persists, at least asymptotically, systems are regularized (i.e. modelled smooth transition (ii)).