A Nonlinear Theory for the Oregonator Model with an External Input

An approximate nonlinear theory of the Oregonator model is obtained with the aid of an ordinary perturbation method when the system is perturbed by some kinds of external input. The effects of internal and external parameters on the oscillations are discussed in detail by taking specific values of the parameters. A simple approximate solution for the Oregonator model under the influence of a constant input is obtained and the result is compared with the numerical result. For other types of external inputs the approximate solutions up to the fourth order expansion are compared with the numerical results. For a periodic input, we found that the entrainment depends crucially on the difference between the internal and external frequencies near the bifurcation point.