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After the successful solid state implementation of memristors, a lot of attention has been drawn to the study of memristor based chaotic circuits. In this paper, a systematic study of chaotic behavior in such system is performed with the help of nonlinear tools such as bifurcation diagrams, power spectrum analysis, and Lyapunov exponents. In particular, a Twin-T notch filter feedback controller is designed and employed to control the chaotic behavior in the memristor based chaotic circuit. Both simulation and experiment results validate the proposed control method.