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The twin-peaked (bimodal) shape of the distribution of per capita income is an intensively discussed topic in economic growth research. The data show that the world income distribution starts with an unimodal structure in 1960 and evolves subsequently towards a bimodal or twin-peaked structure. This empirical result can be replicated by a theoretically based synergetic model using the master equation approach. The present paper extends this discussion by trying to find direct empirical evidence for the mechanism of the theoretical model. We empirically determine the transition rates used in the synergetic approach by applying alternatively nls to a priori specified functional forms and genetic programming in order to determine the parameters simultaneously with the functional forms. Plugging the so determined transition rates into the synergetic model leads in both cases to the emergence of the bimodal distribution which, however, appears to be only a transitory phenomenon.