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Anomaly detection for non-linear dynamical system plays an important role in ensuring the system stability. However, it is usually complex and has to be solved by large-scale simulation which requires extensive computing resources. In this paper, we propose a novel anomaly detection scheme in non-linear dynamical system based on Long Short-Term Memory (LSTM) to capture complex temporal changes of the time sequence and make multi-step predictions. Specifically, we first present the framework of LSTM-based anomaly detection in non-linear dynamical system, including data preprocessing, multi-step prediction and anomaly detection. According to the prediction requirement, two types of training modes are explored in multi-step prediction, where samples in a wall shear stress dataset are collected by an adaptive sliding window. On the basis of the multi-step prediction result, a Local Average with Adaptive Parameters (LAAP) algorithm is proposed to extract local numerical features of the time sequence and estimate the upcoming anomaly. The experimental results show that our proposed multi-step prediction method can achieve a higher prediction accuracy than traditional method in wall shear stress dataset, and the LAAP algorithm performs better than the absolute value-based method in anomaly detection task.