Pattern formation in systems with multiple delayed feedbacks

Abstract

Dynamical systems with complex delayed interactions arise commonly when propagation times are significant, yielding complicated oscillatory instabilities. In this Letter, we introduce a class of systems with multiple, hierarchically long time delays, and using a suitable space-time representation we uncover features otherwise hidden in their temporal dynamics. The behaviour in the case of two delays is shown to ''encode'' two-dimensional spiral defects and defects turbulence. A multiple scale analysis sets the equivalence to a complex Ginzburg-Landau equation, and a novel criterium for the attainment of the long-delay regime is introduced. We also demonstrate this phenomenon for a semiconductor laser with two delayed optical feedbacks.

References in corpus (6)

• The World of the Complex Ginzburg-Landau Equation
• Phase Diagram of the Two-Dimensional Complex Ginzburg-Landau Equation
• Scalable parallel physical random number generator based on a superluminescent LED
• Strong and weak chaos in nonlinear networks with time-delayed couplings
• Crowd synchrony and quorum sensing in delay-coupled lasers
• Decomposing the dynamics of heterogeneous delayed networks with applications to connected vehicle systems

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• Evidence of a critical phase transition in a purely temporal dynamics with long-delayed feedback
• Excitable wave patterns in temporal systems with two long delays
• A new spatio-temporal description of long-delayed systems: ruling the dynamics
• Phases dynamics in VCSELs with delayed optical feedback and cross re-injection
• Spatio-temporal representation of long-delayed systems: an alternative approach
• Classification of coupled dynamical systems with multiple delays: Finding the minimal number of delays
• Emulating complex networks with a single delay differential equation
• State space reconstruction of spatially extended systems and of time delayed systems from the time series of a scalar variable
• Dissipative systems with nonlocal delayed feedback control
• Emergence of spatial patterns and synchronization in superconducting time crystals
• Infinite-dimensional Folded-in-time Deep Neural Networks