Scholarlink

<p>For previous research on stochastic dynamics, investigators focused mainly on systems subjected to temporal noise, and established the Fokker–Planck equation (FPE) corresponding to the Langevin equation describing them. In fact, numerous systems driven by spatiotemporal noise exist across biology, physics, chemistry, and related fields. This study analytically investigates an overdamped univariate spatiotemporal system subjected to spatiotemporal noise in the frame of FPE. First, we employ the Taylor expansion of the spatiotemporal <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12648_2025_3626_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">\(\delta\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>δ</mi> </math></EquationSource> </InlineEquation> function to derive the Kramers–Moyal equation. Subsequently, based on the Langevin equation which describes dynamical behavior of the system, the nth-order transition moment of state variable of the system is calculated to acquire the corresponding FPE for the overdamped univariate spatiotemporal stochastic system. Finally, using monostable and bistable systems subjected to spatiotemporal noise as illustrative cases, we demonstrate that their steady state probability distribution functions obtained from the spatiotemporal FPE agree with numerical solutions of the corresponding spatiotemporal Langevin equations, thereby validating the spatiotemporal FPE’s correctness. This research result not only provides an important tool for investigating analytically the systems subjected to the spatiotemporal noise, but also improves further the current stochastic dynamical theories.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

An overdamped univariate system subjected to spatiotemporal noise in the frame of Fokker–Planck equation

  • 期刊论文

  • 发表日期：

    2025年5月23日

查看全文
  • Ying Sun,
  • Linru Nie

摘要

For previous research on stochastic dynamics, investigators focused mainly on systems subjected to temporal noise, and established the Fokker–Planck equation (FPE) corresponding to the Langevin equation describing them. In fact, numerous systems driven by spatiotemporal noise exist across biology, physics, chemistry, and related fields. This study analytically investigates an overdamped univariate spatiotemporal system subjected to spatiotemporal noise in the frame of FPE. First, we employ the Taylor expansion of the spatiotemporal \(\delta\) δ function to derive the Kramers–Moyal equation. Subsequently, based on the Langevin equation which describes dynamical behavior of the system, the nth-order transition moment of state variable of the system is calculated to acquire the corresponding FPE for the overdamped univariate spatiotemporal stochastic system. Finally, using monostable and bistable systems subjected to spatiotemporal noise as illustrative cases, we demonstrate that their steady state probability distribution functions obtained from the spatiotemporal FPE agree with numerical solutions of the corresponding spatiotemporal Langevin equations, thereby validating the spatiotemporal FPE’s correctness. This research result not only provides an important tool for investigating analytically the systems subjected to the spatiotemporal noise, but also improves further the current stochastic dynamical theories.