This article discusses the theoretical foundations and practical importance of using spatial portraits in analyzing the behavior of two-dimensional dynamical systems. The possibilities of graphically representing the states of dynamical systems, determining their stability states, and predicting their long-term behavior are considered.

This article discusses the study of language, both native and foreign, - a personal need that manifests itself in social interaction and communication. The success of communication depends not only on the desire of the speaker to make contact, but also on the ability to realize speech intention, which depends on the degree of proficiency in language units and the ability to use them in specific communication situations (at the same time, knowledge of individual elements of language in itself cannot be attributed to the concept of “proficiency in language as a means of communication”). These conditions of language proficiency constitute the essence of communicative competence, which has been put forward as one of the central categories of communicative linguistics and linguodidactics.