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The paper proposes the elements of a geometric theory of behavior. The basis of this theory is Model Synthesis an end-to-end technology for describing, synthesizing and implementing agent models. Its main achievement – is the formalization of an agent by a mathematical object a species of structure in the sense of N. Bourbaki. Algorithms that implement actions of agents are included in the base sets of this species of structure. Let us consider morphisms of the base sets with the special attention to the actions mappings. It occurs that unrestricted mappings of base sets can radically change system’s behavior. We can use invariants as restrictions of mappings, if demand their preservation under admissible morphisms. As a result, we can obtain a classification of the systems behavior depending on the invariants that persist during the mappings. Key-Words: Complex Systems, Model Synthesis, Geometric Theory, Behavior, Species of Structure, Morphisms, Invariants, Conservation of Laws

Elements of Geometric Theory of Complex Systems Behavior