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In this paper, we investigate the differential game theoretic approach for distributed dynamic cooperative power control in cognitive radio ad hoc networks (CRANETs). First, a payoff function is defined by taking into consideration the tradeoff between the stock of accumulated power interference to the primary networks and the dynamic regulation of the transmit power of secondary users (SUs). Specifically, the payoff function not only reflects the tradeoff between the requirement for quickly finding the stable available spectrum opportunities and the need for better channel conditions, but also reveals the impact of the differentiated types of data traffic on the demand of transmission quality. Then the dynamic power control problem is modeled as a differential game model. Moreover, we convert the differential game model into a dynamic programming problem to obtain a set of optimal strategies of SUs under the condition of the grand coalition. A distributed dynamic cooperative power control algorithm is developed to dynamically adjust the transmit power of SUs under grand coalition. Finally, numerical results are presented to demonstrate the effectiveness of the proposed algorithm for efficient power control in CRANETs.