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We analyze the dynamics of a class B laser with optoelectronic delayed feedback and periodic modulation of the delay time. For the delay-differential model, we describe asymptotically spike regimes with various properties, namely, with inter-spikes intervals greater than delay, less delay, and a mixed type. Sets of initial conditions in an infinite-dimensional phase space are determined for each type of pulsed solutions. The dynamics of each regime is described by the dynamics of a certain finite-dimensional mapping. By computing the maps we obtain the modulation parameters at which the chaotic spiking of desired structure is realized. We demonstrate bistability of chaotic spiking, their intermittence and merge. [ABSTRACT FROM AUTHOR]

Dynamics of laser with time-variable delayed feedback is analyzed in the neighborhood of the equilibrium. For the system, averaged over a rapidly variable, we obtain parameters at which the stationary state is stable. Stabilization of the stationary state due to modulation of the delay can be successful (unsuccessful) in domains adjacent to super (sub-) critical Hopf bifurcation boundaries. In a vicinity of the bifurcation points, stable and unstable periodic solutions are asymptotically described in dependence on the modulation frequency. [ABSTRACT FROM AUTHOR]

We study the dynamics of the differential-difference model of an optoelectronic generator with delayed feedback in three bifurcation cases. Boundary-value problems are obtained which play the role of normal forms. Stationary inhomogeneous solutions of such problems are structures with a profile in the form of a step or several rectangular pulses. The existence of families of the structures, which differ in the number of pulses and/or their symmetry, is shown. Each of these structures corresponds to rectangular oscillations in the source system with delay. The frequencies and amplitudes of such oscillating solutions to the delay equation are determined. The multistability of oscillating solutions is illustrated. The results provide a justification for the spatiotemporal representation of solutions of the delay equation. • The model of an optoelectronic generator with delayed feedback is analyzed. • Bifurcations of infinite dimension are studied in the case of a large delay. • Boundary-value problems are obtained as quasi-normal forms. • Rectangular structures are stationary inhomogeneous solutions of quasi-normal forms. • Justification for spatiotemporal representation of delayed dynamics is provided. [ABSTRACT FROM AUTHOR]