Critical phenomena in stock exchange are regularly occurring and difficult to predict events, often leading to disastrous consequences. The presented paper is devoted to the search and research of early warning signals of critical transitions in stock exchange based on the results of a multifractal analysis of a series of transactions in shares of public companies. We have proposed and justified the use of certain features of behavior of multifractal spectrum shape parameters such as signals. As model time series, on (...) which methods of multifractal analysis were tested, we used a series of the number of unstable sites of the sandpile automaton on the random Erdős–Rényi graph, self-organizing into critical and bistable states. It was found that the early warning signals for both cellular automata and stock exchanges are an increase in the magnitude of the maximum position, a decrease in the width, and a decrease, followed by a sharp increase, in the value of the spectrum asymmetry parameter. (shrink)

We can observe self-organization properties in various systems. However, modern networked dynamical sociotechnical systems have some features that allow for realizing the benefits of self-organization in a wide range of systems in economic and social areas. The review examines the general principles of self-organized systems, as well as the features of the implementation of self-organization in sociotechnical systems. We also delve into the production systems, in which the technical component is decisive, and social networks, in which the social component dominates; (...) we analyze models used for modeling self-organizing networked dynamical systems. It is shown that discrete models prevail at the micro level. Furthermore, the review deals with the features of using continuous models for modeling at the macro level. (shrink)