  The evolution of a system of chemical reactions can be studied, in the
eikonal approximation, by means of a Hamiltonian dynamical system. The fixed
points of this dynamical system represent the different states in which the
chemical system can be found, and the connections among them represent
instantons or optimal paths linking these states. We study the relation between
the phase portrait of the Hamiltonian system representing a set of chemical
reactions with constant rates and the corresponding system when these rates
vary in time. We show that the topology of the phase space is robust for small
time-dependent perturbations in concrete examples and state general results
when possible. This robustness allows us to apply some of the conclusions on
the qualitative behavior of the autonomous system to the time-dependent
situation.
