<p>Based on the Rucklidge system, this paper constructs a two-scale coupled Rucklidge system under low-frequency parameter excitation to study the vibration control problem of the system by a linear dynamic vibration absorber. The stability of the main system before and after coupling with the linear dynamic vibration absorber is analysed, and the time history diagram and phase diagram of the main system are compared to determine whether the vibration absorber has a vibration reduction effect on the main system. The parameter excitation is regarded as a slow variable, and the non-autonomous system is transformed into a generalised autonomous system. The fast–slow analysis method is used to study the regulatory effect of the stability and bifurcation behaviour of the autonomous system on the vibration response of the non-autonomous system. By changing the excitation amplitude and frequency of the parameter excitation, it is further studied whether the linear dynamic vibration absorber has a suppressive effect on the vibration of the main system under different parameter excitations. The research content of this paper provides a theoretical basis for the vibration reduction study of the two-scale system coupled with a linear dynamic vibration absorber.</p>