Rectangular structures in the model of an optoelectronic oscillator with delay

• Published in: Physica. D Vol. 417; p. 132818
• Main Authors: Grigorieva, E.V., Kashchenko, S.A.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01-03-2021
• Subjects: Bifurcation analysis; Delayed feedback; Laser dynamics; Normal form; Wave structures; Wave structures; Bifurcation analysis; Laser dynamics; Normal form; Delayed feedback
• ISSN: 0167-2789; 1872-8022
• DOI: 10.1016/j.physd.2020.132818

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.