Analytical equivalent transformation method for nonlinear stochastic dynamics with multiple noises in high dimensions

Zhu Ping

Chaos, Solitons & Fractals, 2023, vol. 176, issue C

Abstract: In many practical applications, stochastic problems are high dimensionality and multiple noises. The study focuses on developing an analytical approach for processing multi-noise systems in high dimensions, which overcomes the challenge solving stochastic dynamics problems. Applying an analytical equivalent transformation and introducing a new partial differentiation, the author demonstrate a convenient method for obtaining the Fokker–Planck equation corresponding to Langevin dynamics equations for high-dimensional and multi-noise systems. This methodology is applied to analyze the cubic laser model subjected to white noises and the saturation laser model subjected to bounded sine Wiener noise. The results verify the correction, efficiency, and superiority of the method of processing multiple noises in high dimensions. This approach provides a novel framework for solving other practical dynamics problems for high-dimensional and multi-noise systems.

Keywords: High dimensions; Multiple noises; Stochastic dynamics; Equivalent transformation; New partial differentiation; Analytical method (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:176:y:2023:i:c:s0960077923010354

DOI: 10.1016/j.chaos.2023.114134

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