Local dynamics of the model of a semiconductor laser with delay

We study a model of a semiconductor laser with delay. We discuss the stability of the equilibrium and single out bifurcation parameter values. It turns out that resultant critical cases have infinite dimensions. In the cases where the parameter values are close to critical ones, we constructed first-approximation equations for the asymptotic expansions of solution amplitudes. These equations are nonlinear boundary-value problems of parabolic type, containing integral terms in the nonlinearity in some cases. We present asymptotic formulas that relate solutions of the original model to the constructed boundary-value problems.