A reversible, internal adsorption of cations was picked as one of the possible reasons of nonlinear behaviour of ionic transport through single channel in a membrane. The power law scaling in an adsorption term of the overall discrete dynamical equation for current provides an opportunity for implementing the structure-function relationship. The logistic map in the chaotic region was used as a mathematical basis for the description of K+ transport through poly(ethylene terephthalate) (PETP) nuclear filters.