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During the last century the application of mathematical sciences to biological
problems increased a lot. Mathematicians, physicists and biologists began to
study dierent biological situations, human reactions, cellular interactions
and found their cooperation really useful to represent realistically many
mechanisms.
In this work I refer to some mathematical models of brain system neural
interactions; in particular I pay attention to two dierent neural groups,
whose interaction produces the alternation of REM and NON REM phases
during human sleep.
I start from the model of Hobson McCarley (1975); they represented through
a Lotka Volterra system the interaction between two neural groups involved
in REM and NON REM cycle.
In a second step I use the recent interaction model of Kuramoto to obtain
another system for the neurons activity.
Finally, after a chapter of "mathematical tools", I introduce a diusive model
for this interaction, starting from the precedent Kuramoto model.