  In this paper, the transport phenomena of synaptic electric impulses are
considered. The FitzHugh--Nagumo and FitzHugh--Rinzel models appear
mathematically appropriate for evaluating these scientific issues. Moreover,
applications of such models arise in several biophysical phenomena in different
fields such as, for instance, biology, medicine and electronics, where, by
means of nanoscale memristor networks, scientists seek to reproduce the
behavior of biological synapses. The present article deals with the properties
of the solutions of the FitzHugh--Rinzel system in an attempt to achieve, by
means of a suitable ``energy function'', conditions ensuring the boundedness
and existence of absorbing sets in the phase space. The results obtained depend
on several parameters characterizing the system, and, as an example, a concrete
case is considered.
