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Neuro-dinamic modeling of nonlinear non-stationary processes at realization of the methods of computer mathematics on the basis of the modern catastrophe theory

Keywords:

Yu.I. Nechaev – Dr. Sc. (Eng.), Professor, State University of Information Technology, Mechanic and Optic, St.-Petersburg, Russia, Honored Scientist of RF. E-Mail: nechaev@ifmo.mail.ru O.N. Petrov – Ph.D. (Eng.), Associate Professor, Sant-Petersburg State Marine Technical University (SMTU). E-mail: petr_oleg@mail.ru


The problem of modeling and interpretation of nonlinear non-stationary systems (NN-systems) on the basis of the iterated func-tion system (IFS) is considered. The analysis is carried out with reference to a problem of the dynamic of unsinkability control within the limits of the modern catastrophe theory. The computer complex provides interpretation of extreme situations in the multiprocessor computing environment. The developed conceptual decisions provide interpretation of model of interaction using the modified IFS. The offered structure model contains not only operating, but also interpreting components unlike standard IFS. It has allowed carrying out on each step of iterative process the operative control of dynamics of investigated process taking into account features of behavior of NN-system. The system of the nonlinear differential equations describing dynamics of an emer-gency ship under the influence of casual indignations which is modified on the basis of the concept of the minimum description length of A.N.Kolmogorov and a complexity principle is used as mathematical models of interaction. NN-system behavior is con-sidered on the basis of modified IFS and dynamic model of accidents under the influence of pulse processes and at continuous change of dynamics of object and an environment. The effective description of dynamics of NN-system in this case is received by means of the modified Mathieu equation which periodic function is generated on the basis of the nonlinear spatial function dis-playing interaction a component of dynamic catastrophe model. Results of research have allowed finding out prominent features of a problem of interaction at various stages of NN-system evolution in the complex dynamic environment, and also mechanisms of realization of sharing of functions of management and interpretation of modified IFS within the limits of the concept of the ca-tastrophe theory. Research results are used at integration of knowledge of a subject domain of modeling of NN-systems and L-system into the computer program of high-performance computing.
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May 29, 2020

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