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This paper aims to study an improved chaotic dynamical system. The system has a first integral, and the integral curve stratifies the space. After stratification, the system contains two invariant surfaces. It obtains the local dynamics of chaotic dynamical system by studying the invariant surface. And then it acquires the overall dynamics of the chaotic dynamical system on two invariant algebraic surfaces.doi:10.12783/dtcse/cst2017/12591 fatcat:vmcvf5y6y5f7plo2ixekr6f7c4