Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2010-07-06
Phys. Rev. E 81, 016209 (2010)
Nonlinear Sciences
Chaotic Dynamics
13 pages, 8 figures, RevTeX, accepted for publication in Physical Review E
Scientific paper
10.1103/PhysRevE.81.016209
We study the stability of unstable steady states in scalar retarded time-delayed systems subjected to a variable-delay feedback control. The important aspect of such a control problem is that time-delayed systems are already infinite-dimensional before the delayed feedback control is turned on. When the frequency of the modulation is large compared to the system's dynamics, the analytic approach consists of relating the stability properties of the resulting variable-delay system with those of an analogous distributed delay system. Otherwise, the stability domains are obtained by a numerical integration of the linearized variable-delay system. The analysis shows that the control domains are significantly larger than those in the usual time-delayed feedback control, and that the complexity of the domain structure depends on the form and the frequency of the delay modulation.
Gjurchinovski Aleksandar
Urumov Viktor
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