Temporal Dissipative Solitons in Time-Delay Feedback Systems

Author(s)

Yanchuk, Serhiy ^[1] ; Ruschel, Stefan ^[1] ; Sieber, Jan ^[2] ; Wolfrum, Matthias ^[3]

Affiliation

^[1] Tech Univ Berlin, Inst Math, Str 17 Juni 136, D-10623 Berlin - Germany

^[2] CEMPS Univ Exeter, Harrison Bldg, North Pk Rd, Exeter EX4 4QF, Devon - England

^[3] Weierstrass Inst, Mohrenstr 39, D-10117 Berlin - Germany

• Document type: Journal article
• Source: Physical Review Letters; v. 123, n. 5 JUL 31 2019.
• Web of Science Citations: 0

Abstract

Localized states are a universal phenomenon observed in spatially distributed dissipative nonlinear systems. Known as dissipative solitons, autosolitons, and spot or pulse solutions, these states play an important role in data transmission using optical pulses, neural signal propagation, and other processes. While this phenomenon was thoroughly studied in spatially extended systems, temporally localized states are gaining attention only recently, driven primarily by applications from fiber or semiconductor lasers. Here we present a theory for temporal dissipative solitons (TDS) in systems with time-delayed feedback. In particular, we derive a system with an advanced argument, which determines the profile of the TDS. We also provide a complete classification of the spectrum of TDS into interface and pseudocontinuous spectrum. We illustrate our theory with two examples: a generic delayed phase oscillator, which is a reduced model for an injected laser with feedback, and the FitzHugh-Nagumo neuron with delayed feedback. Finally, we discuss possible destabilization mechanisms of TDS and show an example where the TDS delocalizes and its pseudocontinuous spectrum develops a modulational instability. (AU)

• FAPESP's process: 15/50122-0 - Dynamic phenomena in complex networks: basics and applications
• Grantee: Elbert Einstein Nehrer Macau
• Support Opportunities: Research Projects - Thematic Grants