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Fundamental Structure of General Stochastic Dynamical Systems: High‐Dimension Case

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Listed:
  • Haoyu Wang
  • Xiaoliang Gan
  • Wenqing Hu
  • Ping Ao

Abstract

No one has proved that mathematically general stochastic dynamical systems have a special structure. Thus, we introduce a structure of a general stochastic dynamical system. According to scientific understanding, we assert that its deterministic part can be decomposed into three significant parts: the gradient of the potential function, friction matrix and Lorenz matrix. Our previous work proved this structure for the low‐dimension case. In this paper, we prove this structure for the high‐dimension case. Hence, this structure of general stochastic dynamical systems is fundamental.

Suggested Citation

  • Haoyu Wang & Xiaoliang Gan & Wenqing Hu & Ping Ao, 2022. "Fundamental Structure of General Stochastic Dynamical Systems: High‐Dimension Case," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:2596074
    DOI: 10.1155/2022/2596074
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    References listed on IDEAS

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    1. Liu, Yiguang & You, Zhisheng, 2007. "Multi-stability and almost periodic solutions of a class of recurrent neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 554-563.
    2. Pablo Rodríguez-Sánchez & Egbert H van Nes & Marten Scheffer, 2020. "Climbing Escher’s stairs: A way to approximate stability landscapes in multidimensional systems," PLOS Computational Biology, Public Library of Science, vol. 16(4), pages 1-16, April.
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