We introduce natural generalizations of two
well-known dynamical systems, the Sand Piles Model and the Brylawski's
model. We describe their order structure, their reachable
configuration's characterization, their fixed points and their
maximal and minimal length's chains. Finally, we present an
induced model generating the set of unimodal sequences which amongst other corollaries, implies
that this set is equipped with a lattice structure.