Curved O-operator systems

In this paper, we introduce the notion of curved $\mathcal{O}$-operator systems as a generalization of T. Brzezi'{n}ski’s (curved) Rota-Baxter systems, and then investigate their relations with $\mathcal{O}$-operator systems, (tri)dendriform systems, pre-Lie algebras, associative Yang-Baxter pairs and quasitriangular covariant bialgebras.