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