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This paper treats the globally exponential synchronization problem for a new energy resource chaotic system with two scroll attractors via nonlinear feedback of partial states. Nonlinear feedback rules with some variables and two inputs are derived based on Lyapunov stability theory. The most important features are that the synchronization is achieved through the control of some variables and the speed is high. Simulation results show the feasibility of these rules. The comparisons between these control rules and other developed control methods show that the synchronization response is fast.