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Information × Registration Number 0205U007441, 0101U000526 , R & D reports Title Theory of differential equations and nonlinear oscillations popup.stage_title Head Samojlenko Anatolij Mykhajlovych, Registration Date 28-12-2005 Organization Institute of Mathematics of the National Academy of Sciences of Ukraine popup.description2 The global trajectory behavior on toroidal attractor and its neighborhood for the system of differential equations which appeared at the mathematic model of the optic laser oscillation synchronization studies was studied by means of perturbation theory methods. The explicit expression for Poisson-Abel sum and exact equation for coincidence radius of this sum was found for set of polynomials which appeared at the numerical-analytical method building periodical solutions of the nonlinear differential equations. The asymptotic method of integrability one type of the systems of linear differential equations with small parameter near the part of differentials. The problem of invariant set stability under condition its stability for Cauchi data from manifold which include this set was studied. The new method for finding limited solutions on the whole axis in the form of some part of Loran power epsilon series was proposed and coincidence conditions for corresponding Loran power series was obtained. The sufficient and necessary condition for limited on the real axis solution was obtained for weakly nonlinear systems of the differential and difference equations with Netter linear part at the critical case. The exact sufficient conditions of the global stability of null-solution of the nonlinear difference equations with nonlinear right parts which satisfy negative inverse connections was found. The effective and in the some sense optimal "coefficient" characteristics of the unique solvability of the Cauchi problem for multidimensional systems of the linear functional-differential equations mixed type was obtained. The synchronization conditions, dividing on the clasters, Cherry flows appearing conditions for Kuramoto model was obtained. Methods of qualitative investigation of the phase synchronization of the connected Roestler systems and for the systems with delays were proposed. Product Description popup.authors popup.nrat_date 2020-04-02 Close