Temporal dissipative solitons in time-delay feedback systems

Abstract

Localized states are a universal phenomenon observed in spatially distributed dissipative nonlinear systems. Known as dissipative solitons, auto-solitons, 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 pseudo-continuous 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 pseudo-continuous spectrum develops a modulational instability.

arXiv comment5 pages, 4 figures, submitted (revision) supplementary material available at https://doi.org/10.6084/m9.figshare.8269757 source code for reproducing figures 1a,b, 2a, 3a,b,c available at https://doi.org/10.6084/m9.figshare.8241674

References in corpus (12)

• Ultra-weak long-range interactions of solitons observed over astronomical distances
• Topological solitons as addressable phase bits in a driven laser
• Cavity Soliton Laser based on mutually coupled semiconductor microresonators
• DelayAndPeriodicity
• Spatio-temporal phenomena in complex systems with time delays
• Periodic solutions and refractory periods in the soliton theory for nerves and the locust femoral nerve
• Pattern formation in systems with multiple delayed feedbacks
• Spatio-temporal complexity in dual delay nonlinear laser dynamics: chimeras and dissipative solitons
• Dynamics of Temporal Localized States in Passively Mode-Locked Semiconductor Lasers
• Dissipative soliton excitability induced by spatial inhomogeneities and drift
• Bound pulse trains in arrays of coupled spatially extended dynamical systems
• Dissipative solitons for bistable delayed-feedback systems

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• Chaotic Diffusion in Delay Systems: Giant Enhancement by Time Lag Modulation
• Delay-induced self-oscillation excitation in the FitzHugh-Nagumo model: regular and chaotic dynamics
• Topological Localized states in the time delayed Adler model: Bifurcation analysis and interaction law
• Piecewise discretization of monodromy operators of delay equations on adapted meshes
• Spatio-temporal representation of long-delayed systems: an alternative approach
• Non-local and local temporal cavity soliton interaction in delay models of mode-locked lasers
• Spectrum-based stability analysis and stabilization of a class of time-periodic time delay systems
• Emulating complex networks with a single delay differential equation
• Excitability and memory in a time-delayed optoelectronic neuron
• Normal dispersion Kerr cavity solitons: beyond the mean field limit