Dynamic Analysis and Linear Feedback Control of a Three-Dimensional Energy Price System

Abstract

Evolution of energy price presents new characteristics in the time of carbon emissions trading. This study sets up a new three-dimensional Energy Price chaotic system based on the interdependent and mutually restricted evolution relationship among carbon price, energy price, and economic growth during a given economic period. The dynamic behavior of the system is studied. All equilibrium points are unstable for the system under certain parameters. Lyapunov exponents spectrum and bifurcation diagram present the existence of chaos, and numerical simulation shows the chaotic behavior of the dissipative system. Then the linear feedback control method is used to control the system to the original unstable equilibrium point. Numerical simulations verify the correctness of the theoretical analysis.