DEVELOPMENT OF DECOMPOSITION AND NONLINEAR AGGREGATION METHODS

Lebedev Konstantin Andreevich, Shatalova Alevtina Yurievna

In the context of multifactorial research at the intersection of various disciplines, two methodological tools are used to create algorithms for the analysis and modeling of complex systems: the method of decomposition and nonlinear aggregation. The decomposition method is used for the fractal decomposition of multicomponent systems into hierarchical subsets with a lower degree of complexity, which are amenable to individualized analysis. In contrast, nonlinear aggregation is concerned with synthesizing these reduced subsets into a system's architectural design with a higher level of integration, thereby allowing nonlinear relationships and feedbacks within the system to be revealed and quantified. These methodological strategies are not just tools, but key levers for understanding the fundamental mechanisms underlying the dynamics of complex systems. Through the application of decomposition, scientific researchers can identify and isolate critical variables and parameters that have a significant impact on the overall dynamics of the system. Nonlinear aggregation, in turn, provides mechanisms for integrative modeling of these variables, allowing for their interdisciplinary and interdependent properties to be taken into account. This integrated approach provides the opportunity to generate more robust and predictable system models. These methodologies find their practical implementation in various fields of knowledge, ranging from economic theory to environmental and bioinformation studies. In the context of economics, decomposition plays a central role in the study of macroeconomic indicators such as unemployment rates and GDP and their determinants. Nonlinear aggregation, on the other hand, serves as a tool for constructing econometric models that describe complex and nonlinear relationships between economic variables. In the field of ecological studies, decomposition is used to decompose ecosystems into biotic and abiotic components, while nonlinear aggregation is used to model ecological niches and their dynamics. Bioinformatics, concerned with the analysis of complex biological networks, uses decomposition to identify key genes and proteins, and nonlinear aggregation is used to model their functional interactions and metabolic pathways.

Keywords:decomposition, nonlinear aggregation, research, methodology