Classes of properties preserved under morphisms of generalizations of many-sorted algebraic systems in studying dynamics

We develop the method of logical algebraic equations, which is a method for constructing preservation conditions for properties of some generalizations of many-sorted algebraic systems under their mappings to each other. Preservation criteria are formulated in terms of the notion of canonical generalization of these mappings to Bourbaki grades. Algorithms that simplify solutions of logical algebraic equations are used to describe classes of formulas preserved under single-type morphisms.