ul. Sovetskaya 14, Yaroslavl, 150000, Russia
P.G. Demidov Yaroslavl State University
Kashchenko S. A.
The Dynamics of Second-order Equations with Delayed Feedback and a Large Coefficient of Delayed Control
2016, vol. 21, no. 7-8, pp. 811-820
The dynamics of second-order equations with nonlinear delayed feedback and a large coefficient of a delayed equation is investigated using asymptotic methods. Based on special methods of quasi-normal forms, a new construction is elaborated for obtaining the main terms of asymptotic expansions of asymptotic residual solutions. It is shown that the dynamical properties of the above equations are determined mostly by the behavior of the solutions of some special families of parabolic boundary value problems. A comparative analysis of the dynamics of equations with the delayed feedback of three types is carried out.
Grigorieva E. V., Kashchenko S. A.
Dynamics of spikes in delay coupled semiconductor lasers
2010, vol. 15, no. 2-3, pp. 319-327
We derive the discrete maps to describe the dynamics of coupled laser diodes. The maps allow us to find analytically regions of parameters and initial conditions in the functional phase space that correspond to spiking with stable (or nearly stable) phase shift. The method developed is promising for further discussion of controlled switching between periodic states by an impulse injection signal.