Stability analysis of a three-dimensional energy demand-supply system under delayed feedback control

Kun-Yi Yang; Ling-Li Zhang; Jie Zhang

Kybernetika (2015)

  • Volume: 51, Issue: 6, page 1084-1100
  • ISSN: 0023-5954

Abstract

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This paper considers a three-dimensional energy demand-supply system which typically demonstrates the relationship between the amount of energy supply and that of energy demand for the two regions in China. A delayed feedback controller is proposed to stabilize the system which was originally unstable even under some other controllers. The stability properties of the equilibrium points are subsequently analyzed and it is found that the Hopf bifurcation appears under some conditions. By using the center manifold theorem and normal form method, we obtain the explicit formulae revealing the properties of the periodic solutions of Hopf bifurcation to show stabilizing effects of the delayed feedback controller. Numerical simulations illustrate effectiveness of our results.

How to cite

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Yang, Kun-Yi, Zhang, Ling-Li, and Zhang, Jie. "Stability analysis of a three-dimensional energy demand-supply system under delayed feedback control." Kybernetika 51.6 (2015): 1084-1100. <http://eudml.org/doc/276256>.

@article{Yang2015,
abstract = {This paper considers a three-dimensional energy demand-supply system which typically demonstrates the relationship between the amount of energy supply and that of energy demand for the two regions in China. A delayed feedback controller is proposed to stabilize the system which was originally unstable even under some other controllers. The stability properties of the equilibrium points are subsequently analyzed and it is found that the Hopf bifurcation appears under some conditions. By using the center manifold theorem and normal form method, we obtain the explicit formulae revealing the properties of the periodic solutions of Hopf bifurcation to show stabilizing effects of the delayed feedback controller. Numerical simulations illustrate effectiveness of our results.},
author = {Yang, Kun-Yi, Zhang, Ling-Li, Zhang, Jie},
journal = {Kybernetika},
keywords = {a three-dimensional energy demand-supply system; stability; equilibrium point; delayed feedback control; Hopf bifurcation},
language = {eng},
number = {6},
pages = {1084-1100},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Stability analysis of a three-dimensional energy demand-supply system under delayed feedback control},
url = {http://eudml.org/doc/276256},
volume = {51},
year = {2015},
}

TY - JOUR
AU - Yang, Kun-Yi
AU - Zhang, Ling-Li
AU - Zhang, Jie
TI - Stability analysis of a three-dimensional energy demand-supply system under delayed feedback control
JO - Kybernetika
PY - 2015
PB - Institute of Information Theory and Automation AS CR
VL - 51
IS - 6
SP - 1084
EP - 1100
AB - This paper considers a three-dimensional energy demand-supply system which typically demonstrates the relationship between the amount of energy supply and that of energy demand for the two regions in China. A delayed feedback controller is proposed to stabilize the system which was originally unstable even under some other controllers. The stability properties of the equilibrium points are subsequently analyzed and it is found that the Hopf bifurcation appears under some conditions. By using the center manifold theorem and normal form method, we obtain the explicit formulae revealing the properties of the periodic solutions of Hopf bifurcation to show stabilizing effects of the delayed feedback controller. Numerical simulations illustrate effectiveness of our results.
LA - eng
KW - a three-dimensional energy demand-supply system; stability; equilibrium point; delayed feedback control; Hopf bifurcation
UR - http://eudml.org/doc/276256
ER -

References

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