One of the main faults of a PWM power converter is linked to losing the operating process stability because of bifurcations. A bifurcation diagram contains information on the evolution of the behavior of a PWM power converter that could be theoretically used to prevent the bifurcations. Surprisingly, applying the bifurcation analysis is not yet typical in engineering practice. One of the reasons seems to be in the fundamental properties of the PWM power converter dynamics caused by the unavoidable uncertainty of its behavior near a bifurcation point. We propose a new approach to estimating this uncertainty. By analyzing a set of experimental bifurcation diagrams, our approach allows to determine both the location of the uncertainty zone and the quantitative regularities of the behavior within this zone. The proposed approach can be applied to design and maintenance, including fault diagnosis, and also to scientific research of the nonlinear dynamics regularities. Our results are experimentally verified by using the "PWM DC drive" setup.

This paper is devoted to the development of the experimental bifurcation analysis in the research of local climate dynamics. In particular, we consider the dynamics of the land surface air temperature in the centennial timescale. The experimental bifurcation analysis supposes the choice of a conceptual model to demonstrate how the observable kinds of dynamical processes can be realized on the whole. We worked on the conceptual model with a variable structure (HDS-model), where the dynamics is determined by the competition between the amplitude quantization and the time quantization. The model originates from the hysteresis regulator with double synchronization (HDS-regulator) proposed in 1970’s to achieve the extreme combination of both efficiency and reliability of energy conversion processes. The HDS-model allows to consider the interplay between several periodical processes instead of chaos and quasi-periodicity in order to excuse the variety of the behaviors observed in the local climate dynamics. In particular, the intermittency seems to be the typical behavior of a local climate system from such viewpoint. Here we continue to verify the HDS-model and continue to develop the idea of the modified bifurcation diagrams to reveal the regularities within the intermittency. In particular, we first build the spatial diagram to summarize the results of the bifurcation analysis of the local climate dynamics in the centennial timescale. We assume that each effect of the regional temperature oscillations (RTO-effect) appears as a certain combination of several effects of the local temperature oscillations (LTO-effects), where each LTO-effect can be revealed by the bifurcation analysis. The possibility to build the modified bifurcation diagrams is provided by the SUC-logic aimed for the synthesis of experimental bifurcation analysis, symbolical analysis, and multidimensional data visualization under the assumption that an annual warming–cooling cycle is the unit to analyze. Since only the historical data of the temperature observations are used, then the results approach as close as possible to the real events. We believe that our research seems to be interesting to estimate the theoretically possible latent abilities and evolution of the local climate dynamics.

The paper completes the cycle of the research devoted to the development of the experimental bifurcation analysis (not computer simulations) in order to answer the following questions: whether qualitative changes occur in the dynamics of local climate systems in a centennial timescale?; how to analyze such qualitative changes with daily resolution for local and regional space-scales?; how to establish one-to-one daily correspondence between the dynamics evolution and economic consequences for productions? To answer the questions, the unconventional conceptual model to describe the local climate dynamics was proposed and verified in the previous parts. That model (HDS-model) originates from the hysteresis regulator with double synchronization and has a variable structure due to competition between the amplitude quantization and the time quantization. The main advantage of the HDS-model is connected with the possibility to describe “internally” (on the basis of the self-regulation) the specific causal effects observed in the dynamics of local climate systems instead of “external” description of three states of the hysteresis behavior of climate systems (upper, lower and transient states). As a result, the evolution of the local climate dynamics is based on the bifurcation diagrams built by processing the data of meteorological observations, where the strange effects of the essential interannual daily variability of annual temperature variation are taken into account and explained. It opens the novel possibilities to analyze the local climate dynamics taking into account the observed resultant of all internal and external influences on each local climate system. In particular, the paper presents the viewpoint on how to estimate economic damages caused by climate-related hazards through the bifurcation analysis. That viewpoint includes the following ideas: practically each local climate system is characterized by its own time pattern of the natural qualitative changes in temperature dynamics over a century, so, any unified time window to determine the local climatic norms seems to be questionable; the temperature limits determined for climate-related technological hazards should be reasoned by the conditions of artificial human activity, but not by the climatic norms; the damages caused by such hazards can be approximately estimated in relation to the average annual profit of each production. Now, it becomes possible to estimate the minimal and maximal numbers of the specified hazards per year in order, first of all, to avoid unforeseen latent damages. Also, it becomes possible to make some useful relative estimation concerning damage and profit. We believe that the results presented in the cycle illustrate great practical competence of the current advances in the experimental bifurcation analysis. In particular, the developed QHS-analysis provides the novel prospects towards both how to adapt production to climatic changes and how to compensate negative technological impacts on environment.

The approach to research the uncertainties and the regularities of nonlinear system behavior is developed in the paper. The peculiarity of the approach is connected with modifying the experimental bifurcation diagrams that allows to identify and to analyze certain aspects of the nonlinear dynamics evolution. The variety and the interrelation of the modified bifurcation diagrams are shown. Attention is focused on estimating the limits of the zone within which the nonlinear system behavior is characterized by the uncertainty and on making visible the particular tendencies of dynamics evolution within this zone. The results obtained on the experimental setup of PWM buck converter are used for illustrations. In particular, the uncertainty zone is assumed to be the unit of measurement to estimate the operating process stability margin. It is demonstrated that the properties corresponding to the practical experience appear as per this assumption.

The paper is devoted to the novel logic (SUC-logic) of the nonlinear dynamics forecasting. The SUC-logic is based on three main points: the special sections (S) to build the 2D projections of multidimensional spaces without the loss of useful information; the special units (U) of measurement to estimate the nonlinear dynamics evolution; the special consecutions (C) to realize the nonlinear dynamics forecasting step-by-step. The fractal approach to forecasting the nonlinear dynamics in real-time together with the approach to build the modified bifurcation diagrams to research the regularities and the uncertainties of the evolution scenarios are developed with the SUC-logic. The physical meaning of the uncertainty zone, the stability margin, the risk estimation, the farthest forecasting and the earliest forecasting are considered from the viewpoint of the nonlinear dynamics aspect. Reasonings and discussions are based on experimental and computational results.