  Investigation of the effect of the dynamical stage of heavy-ion collisions
indicates that the increasing width of the initial isospin distributions is
reflected by a significant modification of the isoscaling slope for the final
isotopic distributions after de-excitation. For narrow initial distributions,
the isoscaling slope assumes the limiting value of the two individual initial
nuclei while for wide initial isotopic distributions the slope for hot
fragments approaches the initial value. The isoscaling slopes for final cold
fragments increase due to secondary emissions. The experimentally observed
evolution of the isoscaling parameter in multifragmentation of hot
quasiprojectiles at E$_{inc}$=50 AMeV, fragmentation of $^{86}$Kr projectiles
at E$_{inc}$=25 AMeV and multifragmentation of target spectators at
relativistic energies was reproduced by a simulation with the dynamical stage
described using the appropriate model (deep inelastic transfer and incomplete
fusion at the Fermi energy domain and spectator-participant model at
relativistic energies) and the de-excitation stage described with the
statistical multifragmentation model. In all cases the isoscaling behavior was
reproduced by a proper description of the dynamical stage and no unambiguous
signals of the decrease of the symmetry energy coefficient were observed.
