  In this work we study kink-antikink and antikink-kink collisions in
hyperbolic models of fourth and sixth order. We compared the patterns of
scattering with known results from polynomial models of the same order. The
hyperbolic models considered here tend to the polynomial $\phi^4$ and $\phi^6$
models in the limit of small values of the scalar field. We show that kinks and
antikinks that interact hyperbolically with fourth order differ sensibly from
those governed by the polynomial $\phi^4$ model. The increasing of the order of
interaction to the sixth order shows that the hyperbolic and polynomial models
give intricate structures of scattering that differ only slightly. The
dependence on the order of interaction are related to some characteristics of
the models such as the potential of perturbations and the number of vibrational
modes.
