Multivariate Multiscale Complexity Analysis of Self-Reproducing Chaotic Systems

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Abstract
Designing a chaotic system with infinitely many attractors is a hot topic. In this paper, multiscale multivariate permutation entropy (MMPE) and multiscale multivariate Lempel–Ziv complexity (MMLZC) are employed to analyze the complexity of those self-reproducing chaotic systems with one-directional and two-directional infinitely many chaotic attractors. The analysis results show that complexity of this class of chaotic systems is determined by the initial conditions. Meanwhile, the values of MMPE are independent of the scale factor, which is different from the algorithm of MMLZC. The analysis proposed here is helpful as a reference for the application of the self-reproducing systems.
Funding Information
  • National Natural Science Foundation of China (1174715)
  • the Startup Foundation for Doctoral Research in Hunan University of Arts and Science (E07016048)
  • the Natural Science Foundation of the Higher Education Institutions of Jiangsu Province (16KJB120004)
  • The Startup Foundation for Introducing Talent of NUIST (2016205)

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