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Memory functions of the additive Markov chains: applications to complex dynamic systems

Author

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  • Melnyk, S.S.
  • Usatenko, O.V.
  • Yampol'skii, V.A.

Abstract

A new approach to describing correlation properties of complex dynamic systems with long-range memory based on a concept of additive Markov chains (Phys. Rev. E 68 (2003) 061107) is developed. An equation connecting the memory and correlation function of the system under study is presented. This equation allows reconstructing a memory function using a correlation function of the system. Effectiveness and robustness of the proposed method is demonstrated by simple model examples. Memory functions of concrete coarse-grained literary texts are found and their universal power-law behavior at long distances is revealed.

Suggested Citation

  • Melnyk, S.S. & Usatenko, O.V. & Yampol'skii, V.A., 2006. "Memory functions of the additive Markov chains: applications to complex dynamic systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 361(2), pages 405-415.
    • Handle: RePEc:eee:phsmap:v:361:y:2006:i:2:p:405-415
    DOI: 10.1016/j.physa.2005.06.083
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    Cited by:

    1. Wu, Sheng-Jhih & Chu, Moody T., 2017. "Markov chains with memory, tensor formulation, and the dynamics of power iteration," Applied Mathematics and Computation, Elsevier, vol. 303(C), pages 226-239.

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