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This work is intended as an attempt to extend the notion of bialgebra for Liealgebras to Leibniz algebras and also, the correspondence between the Leibnizbialgebras and its dual is investigated. Moreover, the coboundary Leibnizbialgebras, the classical $r$-matrices and Yang-Baxter equations related to theLeibniz algebras are defined, and some examples are given. Finally, a methodfor construction of a dynamical system on a Leibniz manifold via Leibnizbialgebra is presented.

Leibniz bialgebras, classical Yang-Baxter equations and dynamical systems