In this paper we show the results of the numerical simulation of a "standard" reaction process obtained by a "non standard" system: a reactant oscillator (a harmonic oscillator with an energy threshold) weakly interacting with a unidimensional tent map. According to the paper by M. Bianucci, R. Mannella, B.J. West, and P. Grigolini [Phys. Rev. E 51, 3002 (1995)]], the action of such a map on the reactant system should be equivalent, in some sense, to that of a thermal bath, where the values of the temperature and of the friction depend on the normalized correlation function and on the response function of the map. Here this prediction is confirmed by the numerical simulation. The numerical results are fitted very well by an Arrhenius law with the predicted temperature and friction values. Notice that this is a strict test of the theory because the reaction rate strongly depends on the fine level statistics, i.e., a small deviation in the cue of the distribution would result in a large deviation in the value of the rate.