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The article substantiates the assumptions, axioms and theorems of the universal conflict model – the mathematical apparatus of the unified theory of conflict. The conflict is formalized as a loop of negative feedback, which, depending on the value of the feedback coefficient, can have both linear and nonlinear dynamics. In the first case attractors are of a constant or oscillating character. In the second case, the system tends to chaos and self-destruction. Rationality of axiomatization is caused by the absence in the modern scientific literature of a correct definition of conflict and, as a consequence, a correct understanding of its structure, functions and dynamics. The main advantage of the proposed axiomatization of the conflict is that it opens the way to uniting the unified theory of conflict being developed by the author with the mathematical theory of catastrophes, and the theory of complexity.