Dynamics of Lang-Kobayashi Equations with Large Control Coe cient

We study the system of delayed di˙erential equations modeling the dynamics of semiconductor laser with optical feedback (Lang-Kobayashi model). In the case of instability of external cavity modes we derive the ensembles of quasi-normal forms which appear to be the parabolic (or degenerate parabolic) partial di˙erential equations for slowly varied amplitude of the electric field. Coexistence of a large number of multi-frequency oscillatory regimes is discussed

Dynamics of Lang-Kobayashi Equations with Large Control Coe cient

We study the system of delayed di˙erential equations modeling the dynamics of semiconductor laser with optical feedback (Lang-Kobayashi model). In the case of instability of external cavity modes we derive the ensembles of quasi-normal forms which appear to be the parabolic (or degenerate parabolic) partial di˙erential equations for slowly varied amplitude of the electric field. Coexistence of a large number of multi-frequency oscillatory regimes is discussed

Asymptotic representation of relaxation oscillations in lasers

In this book we analyze relaxation oscillations in models of lasers with nonlinear elements controlling light dynamics. The models are based on rate equations taking into account periodic modulation of parameters, optoelectronic delayed feedback, mutual coupling between lasers, intermodal interaction and other factors. With the aim to study relaxation oscillations we present the special asymptotic method of integration for ordinary differential equations and differential-difference equations. As a result, they are reduced to discrete maps. Analyzing the maps we describe analytically such nonlinear phenomena in lasers as multistability of large-amplitude relaxation cycles, bifurcations of cycles, controlled switching of regimes, phase synchronization in an ensemble of coupled systems and others. The book can be fruitful for students and technicians in nonlinear laser dynamics and in differential equations

Proceedings Of The 23Rd Paediatric Rheumatology European Society Congress: Part Two

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