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Aiming to real easy application in several quadruped robot platforms, this paper introduces a new method of modeling central pattern generators (CPG) to control quadruped locomotion. Not only can this new model generate all the primary gaits of quadrupeds stably with limit cycle effect, but it also has the ability of tuning the periodic outputs with arbitrary waveforms. The core idea is to combine strong points of two mathematical tools: Fourier series and Recurrent neural networks. In addition, a new biomimetic controller is also introduced using the proposed CPG model and several reflex modules. Finally, dynamic simulations are performed to validate the efficiency of the proposed controller.