Serdyk O. Modeling of the critical and crisis phenomena in complex economic systems

In the thesis the model of damped oscillations is developed with the goal of the time series wavelet decomposition surface analysis. This allows ones to define the parameters of the differential equation that describes the nature of the wavelet coefficients at a given scale changes, to assess the current state of the system and prevent a possible transition to a critical state. The method of the theory of random matrices that allows to evaluate the internal state of the economic system during critical phenomena and draw conclusions regarding prejudice and its prevention is improved. The method of multifractal analysis of detrended fluctuations applying, which allows to analyze the complexity of the economic system changes during its evolution and on its basis to assess the current state of the economic system to the premature introduction of measures regulation system to prevent a critical condition is improved. The method of application of graph theory to analyze complex systems through dynamic assessment parameter for determining recurrence of connectivity graph in the process of transformation in the time series graph using the method of cross-recurrent analysis, which allows to increase the accuracy of the current state of the economic system in order to control its development, is improved. The process of economic systems monitoring, thus improving the accuracy of prediction of critical phenomena is improved.