Exploring chaotic attractors in nonlinear dynamical system under fractal theory

This paper introduces a new method to exploit chaotic attractors of nonlinear dynamics. The method decreases both the correlation and the noise of samples while preserves chaotic characteristics of samples in real time applications. The fractal prediction method is used to compressive sensing method in order to concentrate the sparse data on a trajectory. The proposed method can be applied to chaotic noise reduction, signal compression, and object's movement synthesis in video. The experimental results indicate that the proposed method outperforms other state-of-the-art methods. Moreover, the results demonstrate that the chaotic extraction method is most effective to represent a chaotic dynamics of nonlinear time series for signal processing.