Kybernetika 51 no. 6, 1084-1100, 2015

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

Kun-Yi Yang, Ling-Li Zhang and Jie ZhangDOI: 10.14736/kyb-2015-6-1084

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.

Keywords:

stability, Hopf bifurcation, equilibrium point, a three-dimensional energy demand-supply system, delayed feedback control

Classification:

93D05, 93C15, 93C05, 93C95, 93D15

paper.pdf

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