  In this paper we study the differential systems on Leibniz algebroids. We
introduce a class of almost metriplectic manifolds as a special case of Leibniz
manifolds. Also, the notion of almost metriplectic algebroid is introduced.
These types of algebroids are used in the presentation of associated
differential systems. We give some interesting examples of differential systems
on algebroids and the orbits of the solutions of corresponding systems are
established.
