Control of unstable steady states in neutral time-delayed systems |
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Authors: | K B Blyuss Y N Kyrychko P Hövel E Schöll |
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Institution: | 1. Department of Engineering Mathematics, University of Bristol, Bristol, BS8 1TR, UK 2. Institut für Theoretische Physik, Technische Universit?t Berlin, 10623, Berlin, Germany
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Abstract: | We present an analysis of time-delayed feedback control used to stabilize an unstable steady state of a neutral delay differential
equation. Stability of the controlled system is addressed by studying the eigenvalue spectrum of a corresponding characteristic
equation with two time delays. An analytic expression for the stabilizing control strength is derived in terms of original
system parameters and the time delay of the control. Theoretical and numerical results show that the interplay between thecontrol
strength and two time delays provides a number of regions in the parameter space where the time-delayed feedback control can
successfully stabilize an otherwise unstable steady state. |
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Keywords: | PACS" target="_blank">PACS 02 30 Ks Delay and functional equations 05 45 Gg Control of chaos applications of chaos |
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