Advances in Dynamical Systems Theory, Models, Algorithms and Applications最新文献

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Text Mining for Industrial Machine Predictive Maintenance with Multiple Data Sources 基于多数据源的工业机器预测性维护文本挖掘
Advances in Dynamical Systems Theory, Models, Algorithms and Applications Pub Date : 2021-03-19 DOI: 10.5772/INTECHOPEN.96575
Alberto Postiglione, G. Nota
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引用次数: 0
Invariants for a Dynamical System with Strong Random Perturbations 具有强随机扰动的动力系统的不变量
Advances in Dynamical Systems Theory, Models, Algorithms and Applications Pub Date : 2021-02-23 DOI: 10.5772/INTECHOPEN.96235
E. Karachanskaya
{"title":"Invariants for a Dynamical System with Strong Random Perturbations","authors":"E. Karachanskaya","doi":"10.5772/INTECHOPEN.96235","DOIUrl":"https://doi.org/10.5772/INTECHOPEN.96235","url":null,"abstract":"In this chapter we consider the invariant method for stochastic system with strong perturbations, and its application to many different tasks related to dynamical systems with invariants. This theory allows constructing the mathematical model (deterministic and stochastic) of actual process if it has invariant functions. These models have a kind of jump-diffusion equations system (stochastic differential Itô equations with a Wiener and a Poisson paths). We show that an invariant function (with probability 1) for stochastic dynamical system under strong perturbations exists. We consider a programmed control with Prob. 1 for stochastic dynamical systems – PSP1. We study the construction of stochastic models with invariant function based on deterministic model with invariant one and show the results of numerical simulation. The concept of a first integral for stochastic differential equation Itô introduce by V. Doobko, and the generalized Itô – Wentzell formula for jump-diffusion function proved us, play the key role for this research.","PeriodicalId":165968,"journal":{"name":"Advances in Dynamical Systems Theory, Models, Algorithms and Applications","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123406828","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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