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On bifurcation of extremals of one class of variational calculus tasks with multiparametrical perturbation

Ashimov A. A., Sagadiyev K. A., Borovskiy Y. V., Iskakov N. A., Ashimov A. A.

Systems Science

2007

Vol. 33, no 4

85-91

A bifurcation of the extremals of one variational calculus task on the choice of optimum laws for a parametrical regulation of a dynamic system in the given finite set of algorithms is under consideration. An assertion about conditions sufficient for the existence of the specified variational calculus task's solution is formulated and proved. A defintion of a bifurcation point under a multiparametrical perturbation of the given variational calculus task is provided. An assumption on the sufficient conditions for its existence is formulated and proved. A numerical algorithm of calculating a bifurcation value of a parameter is offered. The findings are illustrated by the example of calculated set of bifurcation points of the extremals of the variational calculus task on the choice of optimum laws for a parametrical regulation of the market economy mechanisms in the given finite set of algorithms on the basis of a mathematical model of the economic system of the country, which is suggested in order to investigate the influence of state expenditures upon its evolution. The research findings could be applied to the process of development and implementation of an effective state economic policy.