Differential Algebraic Framework for Synergetics: A Constructive Approach to Order Parameters and Macroscopic Behavior

Differential Algebraic Framework for Synergetics: A Constructive Approach to Order Parameters and Macroscopic Behavior | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 31 October 2025 V1 Latest version Share on Differential Algebraic Framework for Synergetics: A Constructive Approach to Order Parameters and Macroscopic Behavior Author : shifa liu 0009-0003-6570-2812 [email protected] Authors Info & Affiliations https://doi.org/10.22541/au.176194051.10448917/v1 181 views 134 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract 本文为协同复杂系统的建设性分析建立了全面的微分代数框架。在随机分析、泛函分析和重整化群论的严格数学基础上，我们通过精心构建的递归附加过程定义协同微分闭包 K Syn。这种闭包系统地结合了阶参数、从属原理、波动修正和宏观几何结构，为研究涌现行为提供了一个统一的数学宇宙。我们提供完整的随机微分场扩展，具有精确的过滤结构、具有误差边界的严格中心流形结构，以及在此闭包中详细的威尔逊重整化群分析。该框架严格解决非线性、多尺度相互作用和随机波动问题，同时通过数学上精确的公式保留协同的基本原理。 Supplementary Material File (synergetics_theory.pdf) Download 383.22 KB Information & Authors Information Version history V1 Version 1 31 October 2025 Copyright This work is licensed under a Creative Commons Attribution 4.0 International License Keywords complex systems critical phenomena differential algebraic closure pattern formation renormalization group reorder parameters slaving principle synergetics Authors Affiliations shifa liu 0009-0003-6570-2812 [email protected] View all articles by this author Metrics & Citations Metrics Article Usage 181 views 134 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation shifa liu. 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