Transport Phenomena in Excitable Systems: Existence of Bounded Solutions and Absorbing Sets

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 such arise in several biophysical different fields as, instance, biology, medicine electronics, where, by means nanoscale memristor networks, scientists seek to reproduce behavior biological synapses. present article deals with properties solutions system an attempt achieve, a suitable ``energy function'', conditions ensuring boundedness existence absorbing sets phase space. results obtained depend on parameters characterizing system, and, as example, concrete case is