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Nonlinear stochastic dynamics have been studied for over sixty years and are theoretically well-developed, but many challenges still remain. The achievements in nonlinear stochastic dynamics are mainly based on the research results of Markov process and its related theory of stochastic differential equationStochastic differential equation (SDE) in mathematics. The only case in nonlinear stochastic dynamics that can be exactly solved is that excitation is white noise and the system responseSystem response is Markov process with transition probability density governed by Fokker–Planck-Kolmogorov (FPK) equation.

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Introduction

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  • 发表日期：

    2025年

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  • Wei-Qiu Zhu,
  • Mao-Lin Deng,
  • Guo-Qiang Cai

摘要

Nonlinear stochastic dynamics have been studied for over sixty years and are theoretically well-developed, but many challenges still remain. The achievements in nonlinear stochastic dynamics are mainly based on the research results of Markov process and its related theory of stochastic differential equationStochastic differential equation (SDE) in mathematics. The only case in nonlinear stochastic dynamics that can be exactly solved is that excitation is white noise and the system responseSystem response is Markov process with transition probability density governed by Fokker–Planck-Kolmogorov (FPK) equation.