Hopf bifurcation control for a class of delay differential systems with discrete-time delayed feedback controller

Su, Huan and Mao, Xuerong and Li, Wenxue (2016) Hopf bifurcation control for a class of delay differential systems with discrete-time delayed feedback controller. Chaos: An Interdisciplinary Journal of Nonlinear Science, 26 (11). pp. 1-20. ISSN 1054-1500 (https://doi.org/10.1063/1.4968557)

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Abstract

This paper is concerned with asymptotical stabilization for a class of delay differential equations, which undergo Hopf bifurcation at equilibrium as delay increasing. Two types of controllers, continuous-time and discrete-time delay feedback controllers, are presented. Although discrete-time control problems have been discussed by several authors, to the best of our knowledge, so few controllers relate to both delay and sampling period, and the method of Hopf bifurcation has not been seen. Here, we first give a range of control parameter which ensures the asymptotical stability of equilibrium for the continuous time controlled system. And then, for the discrete-time controller we also obtain an efficient control interval provided that the sampling period is sufficiently small. Meanwhile, we try our best to estimate a well bound on sampling period and get a more complete conclusion. Finally, the theoretical results are applied to a physiological system to illustrate the effectiveness of the two controllers.

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