An integro-differential model of the generation dynamics of a large laser chain with two-way optoelectronic coupling via pumping is investigated. Critical values of the coupling coefficient and delay time in the coupling lines are obtained, at which dual- and multi-frequency quasi-periodic oscillations of the radiation intensity can occur.

Methods of study. Local dynamics studies based on constructing normal forms on central manifolds are applied to critical cases of (asymptotically) infinite dimension. An algorithm for reducing the original boundary value problem to equations for slowly varying amplitudes is proposed. A system of complex Ginzburg-Landau equations is constructed as a quasi-normal form (QNF). The nonlocal dynamics of these equations determines the behavior of the solutions to the original boundary value problem.

Results obtained. Homogeneous solutions of the CNF and corresponding solutions of the nonlinear chain model were obtained. These can be interpreted as quasi-periodic oscillations and a regime of alternating in-phase and anti-phase generation modes in bidirectionally
coupled lasers. The frequencies and amplitudes of the laser intensity oscillations in the chain were calculated.