Journal
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
Volume 18, Issue 6, Pages 1759-1765Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218127408021348
Keywords
nonlinear dynamical system; control; delayed feedback; multistability
Funding
- DFG [Sfb 555]
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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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