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

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  • Haoyu Wang
  • Xiaoliang Gan
  • Wenqing Hu
  • Ping Ao
  • M. M. Bhatti

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 & M. M. Bhatti, 2022. "Fundamental Structure of General Stochastic Dynamical Systems: High-Dimension Case," Journal of Mathematics, Hindawi, vol. 2022, pages 1-24, June.
    • Handle: RePEc:hin:jjmath:2596074
    DOI: 10.1155/2022/2596074
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