Yanchuk S. V.
Ukr. Mat. Zh. - 2008. - 60, № 3. - pp. 426–435
We consider a system of ordinary differential equations used to describe the dynamics of two coupled single-mode semiconductor lasers. In particular, we study solutions corresponding to the amplitude synchronization. It is shown that the set of these solutions forms a three-dimensional invariant manifold in the phase space. We study the stability of trajectories on this manifold both in the tangential direction and in the transverse direction. We establish conditions for the existence of globally asymptotically stable solutions of equations on the manifold synchronized with respect to the amplitude.
Conditions for exponential stability and dichotomy of pulse linear extensions of dynamical systems on a torus
Ukr. Mat. Zh. - 1998. - 50, № 3. - pp. 451–453
Conditions for exponential stability and dichotomy of pulse linear extensions of dynamical systems on a torus are investigated.
On the behavior of solutions of the equation for components of a normal system of differential equations
Ukr. Mat. Zh. - 1997. - 49, № 10. - pp. 1436–1440
We obtain necessary and sufficient conditions for the existence of a sliding mode and also for the knotting of solutions of the equation for components of a normal system of first-order differential equations.
Ukr. Mat. Zh. - 1997. - 49, № 4. - pp. 591–596
We study rotary motions for an autonomous second-order differential equation with pulse influence and periodic right-hand side and indicate some important properties of these motions. By using the numerical-analytic method, we establish sufficient conditions for the existence of rotary motions.