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Delay-induced multistability near a global bifurcation

J. Hizanidis·R. Aust·E. Schoell
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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.

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J. Hizanidis, R. Aust, E. Schoell. 2007-04-10. Delay-induced multistability near a global bifurcation. https://doi.org/10.1142/s0218127408021348

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