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The approach to the formation of a multidimensional digital model of the learning environment using the mathematical unit of differential equations of the first order, implemented on the system of systems principle is considered. It is shown that within the framework of digitalization of the main components of this environment, bifurcation analysis can be carried out to detect fuzzy and under-defined learning results that do not depend directly on either the teachers or the learner. In other words, it has been found the source of the strange attractors of the learning environment as a complex nonlinear open system, which essentially depends on the initial conditions. Such situations may arise while simultaneous using old, well-established teaching methods and some new digital tools to form knowledge of learners. The results of modeling of such situations are discussed, approaches to neutralize this kind of fuzziness are considered.