Perturbation Theory of Self-Oscillating System with a Periodic Perturbation

If a small periodic perturbation is applied to the self-oscillating system, it will, in some cases, entrain the system, in other cases, the system oscillates independently. These behaviours are examined numerically by Tomita et al. in a famous model chemical reaction–Brusselator. In this paper, a perturbation method is applied to obtain analytically the behaviour of the system under a periodic perturbational force. This method is applicable near the onset of the limit cycle oscillations.