2019
Том 71
№ 1

All Issues

Yanchuk S. V.

Articles: 4
Article (Russian)

Amplitude synchronization in a system of two coupled semiconductor lasers

Lykova O. B., Schneider K. R., Yanchuk S. V.

↓ Abstract   |   Full text (.pdf)

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.

Brief Communications (Russian)

Conditions for exponential stability and dichotomy of pulse linear extensions of dynamical systems on a torus

Ali N. A., Yanchuk S. V.

↓ Abstract   |   Full text (.pdf)

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.

Article (Ukrainian)

On the behavior of solutions of the equation for components of a normal system of differential equations

Yanchuk S. V.

↓ Abstract   |   Full text (.pdf)

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.

Brief Communications (Russian)

Rotary motions of autonomous systems with pulse influence

Ali N. A., Yanchuk S. V.

↓ Abstract   |   Full text (.pdf)

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.