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.