The paradigm of nonlinearity and the aggression of the russian federation against Ukraine
Authors:   Lviv Polytechnic National University, Hunko Leonid 
Published: February 2023

The understanding of the paradigm of nonlinearity in modern conditions as compared to the linear vision of the world is analyzed, the main components of the advantages of the nonlinear approach in armed conflicts are shown, the connection of the nonlinear approach to the conduct of hostilities with the victories of the Armed Forces of Ukraine over the aggressor’s troops in the conditions of a full-scale war of the Russian Federation against Ukraine is substantiated. Formulation of the problem. The full-scale aggression of the Russian Federation against Ukraine which began on February 24, 2022, has proved huge threats to the national security of Ukraine, led to the need to rethink the principles, strategy and tactics of warfare in modern conditions. Changes in the nature of war, which are characterized by uncertainty, unpredictability of the opponents’ behavior, the need to adapt to the surrounding environment, require changes in the conduct of hostilities. Understanding of the nonlinear nature of war will enable the military leadership to make effective decisions at the strategic and tactical levels. Analysis of recent research and publications. While studying the nonlinear nature of war, different approaches can be observed. Thus, Peter Pomerantsev, considering the aggression of the Russian Federation against Ukraine, calls the «hybrid war» a nonlinear one, which he associates with the growing role of non-military methods of conducting the conflict [6]. By analyzing the diffuse war, Hryhoriy Pocheptsov touches the issue of nonlinearity when the understanding of the threat comes only after the consequences. He associates nonlinearity with chaos, since deterministic chaos cannot manifest itself in linear systems. He agrees that a nonlinear war is an attack in many directions at the same time [7]. R. Arzumanian, while investigating the nonlinear nature of war and examining Clausewitz’s theory of war, emphasizes that the latter defined war as a nonlinear phenomenon, the consequence of which is complexity and unpredictability. V.Horbulin in his work «How we can defeat Russia in the war of the future», without speaking directly about the nonlinearity of war, analyzes a number of characteristic features of a nonlinear war. Identification of previously unsolved parts of the general problem. The researchers mentioned above consider important issues related to the nonlinear nature of the war, but the most important question is how the theory gets its justification in the conditions of large-scale aggression of the Russian Federation against Ukraine. The purpose of the study is to analyze the application of the principles of nonlinearity for decision-making by the military generalship of Ukraine in the conditions of real combat operations. Presenting the basic material. The Newtonian or linear vision has recently remained the dominant paradigm in the world that presupposed a classical view of the cause-and-effect relationships of processes and events. The term «paradigm» comes from the Greek word παράδειγμα which means «example, model» and which is understood as a set of fundamental scientific ideas and terms, perceived and shared by the scientific community and is characteristic of a certain period of the development of science. The nonlinear paradigm is understood as the systematization of natural, social phenomena and processes as a nonlinear phenomenon. The main features characterizing the nonlinear paradigm include: the complexity and unpredictability of the system, its adaptability, chaos, openness, sensitivity to initial conditions and a large number of reversed feedback. The process of rethinking of the war from the point of view of a nonlinear paradigm is initiated by military defeats which make us understand the reasons for the defeat, learn a new strategy and tactics in order to adapt to new realities. The full-scale aggression of the Russian Federation against Ukraine is characterized by the fact that the Russian Federation is waging a traditional linear war against Ukraine and using nonlinear approaches to conducting hostilities. The characteristic features of a linear war are: excessive centralization of decision-making at all levels of the military organization; blocking the initiative at grassroots levels in the armed forces; building a war strategy based on direct and proportional connections between causes and consequences, obtaining significant results with the resources involved; a military operation is considered as a closed system; external factors, including possible actions of the opponent, are not fully taken into account during planning. Modern real war is a qualitatively more complex process that involves instability, unpredictability, uncertainty, dynamism and operational efficiency. The characteristic features of non-linear war are: support of the initiative at all levels of the military organization; building strategy and tactics using asymmetric solutions in conditions of limited resources; a war is considered as an unbalanced, open, nonlinear system sensitive to initial conditions with continuous feedback; maneuverability and ‘swarming’ which is understood as combat influence in many directions at the same time. The use of a nonlinear approach to the conduct of hostilities is beginning to yield positive results Conclusions and prospects for further investigations. Based on the fact that the full-scale military aggression of the Russian Federation against Ukraine is taking place in conditions where the Russian Federation and Ukraine use different approaches to planning the implementation of hostilities, it can be argued that Ukraine will gradually win on the battlefield in a conventional war. The issue of developing a nonlinear approach in the formation of strategy and tactics of advancing actions in conditions of war requires further analysis and research.