The mathematical model of the forced synchronization system, composed of four oscillators is investigated. The mathematical model of the system is the matrix differential equation with delayed arguments. The matrix differential equation is solved using method of steps and applying Laplace transform. Using this method and exact solution of the matrix differential equation with delayed arguments was obtained and exact expressions of the elements of the step responses matrix, of the synchronization system are got. On the base of derived formulas the transition processes of the system are investigated.

Darbe nagrinėjamas dvimatis atstatymo procesas. Gaunami jo integralinių lygčių ir laplaso transformacijų pavidalai, bei jų asimptotikos. / In graduate research a two-dimentional renewal process. The integral differential equation of renewal function, its Laplase transform and asymptotic's was found.

The mutual in the synchronization system is analyzed in this work. The mutual in the synchronization is a double – side synchronization of interdependent tactical oscillators. Every of interdependent oscillators has influence on the frequency of other oscillators. The frequency of all oscillators will be the same and equal to the certain medium frequency which depends upon, the frequency and distances among separate oscillators of all in the settled regime of them joined into the net. The objective of the work is to analyze the synchronization system which is joined of four interdependent oscillators. The mathematical model of synchronization system is formed, analytic expressions of transitional function and differences among phases of oscillation are set transitional processes of synchronization system and differences among phases of oscillation are researched. The mathematical model of synchronization system is matrixal rectilinear dif. Equation with the argument to be late. It is solved using the method of steps and the transformation of Laplace. Exact analytical expressions of the solution components are found using Jordan’s form of descriptive matrix which describes the structure of inherent relations among the blocks of the system analytical expressions of transitional functions in the system and differences of phases of oscillation are obtained on the basis of the solution.