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The article investigates the formal models as a method of analysis in international studies. The importance of this type of models in writing articles for world leading high-ranking journals from Scopus list is shown. The author reveals the main challenges of interdisciplinary synthesis related to the construction of formal models. The problem of identifying the actors of international relations is revealed, including the assessment of actor's involvement in a concrete international conflict (or process) in the context of the concepts of defensive and offensive realism, as well as of real and of latent (potential) power. The decrease in the influence of the state as the primary actor in international relations, and the increase of influence of new types of actors are shown, including international terrorist networks (led by IS), political parties, media and NGOs in the context of post-modernism, global business structures. At the national level, the main actors are illustrated both by the example of countries with a developed civil society and a market economy, and by that of the traditional non-Western society. The question of levels of analysis in international relations, as well as agent-structure problem are illustrated by concrete cases from modern international relations. The author describes a model of "nested" politics. The main types of models used in international studies (game theoretic, econometric, network analysis, simulation) are indicated as well as their shortcomings. Two kinds of simulation models - system dynamics and agent-based modeling are described. It is noted that the agent-based modeling is carried out mainly in the framework of the constructivist paradigm of international relations theory.

The nature of cooperation regularly changes under pressure from new calls and threats between the actors of international relations. By means of system analysis and comparison methods, the article discloses the basic theoretical approaches to understanding of the "new world order" phenomenon, which as a result turns into a comprehensive globalization. The article summarizes the modern trends of forming the XXI century international reality, taking into account new actors, their influence on stability and variability of the imperious systems, and analyzes in detail the concepts of modern scientists who form an international discourse on the search for a new paradigm of world order. The study identifies the main characteristics of the world order – legitimacy, the mechanism of change and balance of power. The key shortcomings of the post-war world order have been identified, which include the lack of effectiveness of international organizations at various levels in ensuring the principle of sovereignty for states, respect for borders; imbalance of economic growth between nations; lack of effective sanctions against violators of international law and ensuring the universal rights of citizens; discredited democratic political model, which was recognized as dominant in the post-bipolar era, and so on. Accordingly, there were considered modern approaches to a "new world order" formation, as a result of which it was proposed to take into account the new realities of interdependence that determine the future peaceful coexistence of nations – a balance between freedom of national actors action and international law; balance between legitimacy and power; balance between "regional order" and "international". In general, the international discourse on the search for the "new world order" boundaries is common in the construction of the XXI century multipolar world, the importance of consensus between nations and the legitimacy of new rules for all actors in international relations.