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In this paper, we study the dynamic uplink power allocation problem in a multi-cell multi-user CDMA-based cellular cognitive radio (CR) system, in which the concept of hierarchical interference bound is introduced to describe the coexistence of the multi-user interference. We propose a novel differential game-based dynamic power allocation model via two formulated cost functions. Furthermore, we present a distributed non-cooperative dynamic uplink power allocation algorithm under the condition that the average power limits and the quality of service (QoS) constraints of secondary users (SUs) are guaranteed. Simulation results demonstrate that the proposed algorithm can regulate the transmit power and the throughput of SUs effectively.