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• W1999549244 abstract "Delayed feedback control (DFC), proposed by Pyragas [Phys. Lett. A 170, 421 (1992)], is a simple and practical method of controlling chaos in continuous dynamical systems. However, it had been proved that the DFC has a limitation; that is, any hyperbolic unstable periodic orbit (UPO) with an odd number of real characteristic multipliers greater than unity can never be stabilized by the DFC. In this paper, to overcome this limitation, we propose a modified DFC, ``half-period delayed feedback,'' of which the delay time is a half of the period of the UPO. We apply it to stabilizing self-symmetric directly unstable periodic orbits of the Duffing equation. This modified DFC can also be generalized to a form stabilizing symmetric periodic orbits in some systems with symmetries such as the Lorenz equation." @default.
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• W1999549244 date "1998-08-01" @default.
• W1999549244 modified "2023-10-17" @default.
• W1999549244 title "Half-period delayed feedback control for dynamical systems with symmetries" @default.
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• W1999549244 doi "https://doi.org/10.1103/physreve.58.1757" @default.
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