Delay-induced multistability near a global bifurcation

Abstract

We study the effect of a time-delayed feedback within a generic model for a saddle-node bifurcation on a limit cycle. Without delay the only attractor below this global bifurcation is a stable node. Delay renders the phase space infinite-dimensional and creates multistability of periodic orbits and the fixed point. Homoclinic bifurcations, period-doubling and saddle-node bifurcations of limit cycles are found in accordance with Shilnikov's theorems.

Int. J. Bif. Chaos (2007), in print

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• Stabilizing continuous-wave output in semiconductor lasers by time-delayed feedback
• Synchronisation in networks of delay-coupled type-I excitable systems
• Control of coherence resonance in semiconductor superlattices
• Pulse-timing symmetry breaking in an excitable optical system with delay
• Delay-induced self-oscillation excitation in the FitzHugh-Nagumo model: regular and chaotic dynamics