{"title":"Numerical analysis of the stochastic FitzHugh–Nagumo model driven by multiplicative noise based on the spectral Galerkin method","authors":"Rushuang Yang , Huanrong Li","doi":"10.1016/j.rinam.2024.100477","DOIUrl":null,"url":null,"abstract":"<div><p>The stochastic FitzHugh–Nagumo (FHN) neural information transduction model has been widely used in different fields, but there are few numerical studies on this model. In this paper, the stochastic FHN model driven by multiplicative noise is studied based on the spectral Galerkin method. The model is firstly discreted by semi-implicit Euler–Maruyama scheme in time and spectral Galerkin method in space. The error estimation and convergence order are then analyzed. Finally, the one-dimensional and two-dimensional stochastic FHN models are numerically calculated and the convergence order is verified. Moreover, this study promotes the understanding of the information transmission law of neural information transmission model under the influence of stochastic factors.</p></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"23 ","pages":"Article 100477"},"PeriodicalIF":1.4000,"publicationDate":"2024-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2590037424000475/pdfft?md5=953719a9089f7a91744ddf3bfd2f302c&pid=1-s2.0-S2590037424000475-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Results in Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2590037424000475","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
The stochastic FitzHugh–Nagumo (FHN) neural information transduction model has been widely used in different fields, but there are few numerical studies on this model. In this paper, the stochastic FHN model driven by multiplicative noise is studied based on the spectral Galerkin method. The model is firstly discreted by semi-implicit Euler–Maruyama scheme in time and spectral Galerkin method in space. The error estimation and convergence order are then analyzed. Finally, the one-dimensional and two-dimensional stochastic FHN models are numerically calculated and the convergence order is verified. Moreover, this study promotes the understanding of the information transmission law of neural information transmission model under the influence of stochastic factors.
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