E.V. Grigorieva, S.A. Kashchenko "Rectangular structures in the model of an optoelectronic  oscillator with delay" Physica D: Nonlinear Phenomena vol 417, 132818 (2021)

https://doi.org/10.1016/j.physd.2020.132818

Abstract

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.