干旱区生态环境知识资源中心

One of the most illustrative examples of promising applications of the practice-oriented bifurcation analysis concerns forecasting. We focus on emergency forecasting for pulse energy conversion systems (PEC-systems). In this case it becomes necessary to integrate regularities from both phase and parametrical spaces and demands on the operating stability and performance, taking into account the critical demand to uninterrupted analytics during steady states and transients. Thus so-called conflict-of-units between the notions used to understand natural evolution (for example, the evolution connected with the operating process) and the notions used to describe desirable artificial regimes (for example, the operating regime) should be resolved. With this purpose, we attract a specific integrating analytics (bifurcation-fractal analytics), the basis of which is provided by modified bifurcation diagrams arid fractal regularities. Here the fractal regularities mirror geometrical similarities between shapes of limit cycles and mirror regular dimensional modifications of these shapes with parametrical variation. Modified bifurcation diagrams provide the conciliation of the practicing and scientific notions without distortions and losses of the useful information from parametrical and phase spaces. Then multi-D conflict-free correspondence between causes (degradation of the operating process stability) and effects (changes of the operating regime characteristics) is established, and empirical recommendations on the operating performance can be substituted by clear nonlinear regularities. Fractal methods of real-time forecasting during transients are included in the discussion and their adaptation to the emergency forecasting is proposed. It opens a novel way on how to forecast the operating stability and performance on the common basis of nonlinear regularities which indicate the operating changes towards emergencies. The discussion is illustrated by computer-based and experimental examples. We believe that the results seem to be interesting to researchers in the field of the practice-oriented bifurcation analysis.