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依恋理论的计算模型与伴侣互动动力学
从焦虑-回避双稳态耦合、戈特曼非线性差分方程到原生家庭先验修正的数学与心理学研究
Computational Attachment Theory and Couple Interaction Dynamics: From Anxious-Avoidant Coupled Oscillators and Gottman's Nonlinear Difference Equations to Updating Early Relational Priors
DOI10.5281/zenodo.23754715摘要
一方想谈、另一方想躲，一方越追问、另一方越沉默——许多伴侣熟悉这种越转越快的回路。本书用依恋理论、动力系统与纵向研究考察它从哪里来、早期经验在多大程度上决定它、以及什么能让它慢下来。依次讨论：鲍尔比与安斯沃思的依恋理论与成人依恋的焦虑、回避两个连续维度（把它们切成「类型」会使约四分之一的人在重测时换标签），以及把内部工作模型写成贝叶斯先验时，先验、对负面证据的加权与采样不足三种偏差的区别；追—逃回路的耦合速率方程（反应敏感度足够高时出现自我维持的升级与周期性爆发，降低任何一方的敏感度效果对称）；戈特曼与默里婚姻差分方程的稳态与吸引域，戈特曼「约 5 比 1」的描述性观察与已被撤回的洛萨达「临界正性比例」的区别，以及离婚预测为什么需要交叉验证；冲突中的生理联动与共调、升级耦合的阈值，以及共同处境造成的假联动；依恋稳定性的真实效应量（元分析平均 r = 0.39，只解释约 15% 的变异，间隔超过 15 年不再显著）、关系对工作模型的可能修正与「后天习得安全」的争议；修复尝试作为阻尼（做出与被接收相乘）与暂停冷静的生理学。
八章与《周易》咸卦「二气感应以相与」与「君子以虚受人」、家人卦、《诗经·击鼓》「死生契阔，与子成说」的两种读法、《大学》「身修而后家齐」与《孟子》「行有不得者，皆反求诸己」并读，并明确古代等级制家庭伦理与现代平等伴侣关系的界限；最后给出一份四步互动回路核查表，以及一项比较「追—逃回路可视化 + 20 分钟生理降温 + 修复用语」结构化会谈与常规沟通指南的预注册伴侣随机对照试验方案（主要结局为一周冲突日记中的升级时长，每组 130 对可分析、招募 163 对，含分别私下进行的亲密伴侣暴力筛查，判定规则写成代码）。书中以标注框区分已发表的证据、可运行的 Python 计算（14 段程序，全部核对）、原典与作者的假说。本书不是婚姻家庭治疗或心理咨询；存在暴力或控制的关系请优先寻求安全与专业帮助。
关键词：依恋理论；依恋焦虑；依恋回避；内部工作模型；贝叶斯先验；要求—退缩；追—逃回路；耦合动力系统；极限环；戈特曼—默里模型；正负比例；洛萨达比例；交叉验证；生理联动；共调；依恋稳定性；后天习得安全；修复尝试；周易；孟子
Abstract
One partner wants to talk, the other wants to get away; the more one presses, the quieter the other becomes. Many couples know this loop that spins faster and faster. This book uses attachment theory, dynamical systems and longitudinal research to ask where it comes from, how far early experience determines it, and what can slow it down. It covers Bowlby's and Ainsworth's attachment theory and the two continuous dimensions of adult attachment, anxiety and avoidance (cutting them into "types" makes about a quarter of people change label on retest), and, with the internal working model written as a Bayesian prior, the difference between bias in the prior, extra weight on negative evidence and too little sampling; coupled rate equations for the pursue–withdraw loop (at high enough sensitivity, self-sustaining escalation and periodic eruptions appear, and lowering either partner's sensitivity has symmetric effects); the steady states and basins of attraction of Gottman and Murray's marriage difference equations, the difference between Gottman's descriptive "about 5 to 1" and Losada's withdrawn "critical positivity ratio", and why divorce prediction needs cross-validation; physiological linkage and co-regulation in conflict, the threshold of escalating coupling, and spurious linkage from a shared situation; the real effect sizes of attachment stability (meta-analytic average r = 0.39, explaining about 15 % of the variance, no longer significant over intervals longer than 15 years), how relationships may revise working models, and the dispute over "earned security"; and repair attempts as damping (making and accepting multiply) and the physiology of taking a break.
The eight chapters are read beside the Book of Changes hexagram Xian ("the two energies respond to each other and draw together", "the noble person receives others with emptiness") and the hexagram Jiaren, the two readings of "in death or life, near or far, I made my pledge with you" from the Book of Songs, the Great Learning's "once the self is cultivated the family is ordered" and Mencius's "whenever an action fails, seek the cause in oneself", stating clearly the boundary between hierarchical classical family ethics and modern equal partnerships. They end with a four-step interaction-loop checklist and a pre-registered couple-randomised controlled trial comparing a structured session (pursue–withdraw loop visualisation, a 20-minute physiological cool-down and repair phrases) with a standard communication guide (primary outcome escalation time in a one-week conflict diary, 130 analysable and 163 recruited couples per arm, separate and private intimate-partner-violence screening, decision rule written as code). Marked boxes separate published evidence, runnable Python calculations (14 programs, all checked), classical sources and the author's hypotheses. This book is not marital or family therapy or counselling; anyone in a relationship with violence or control should seek safety and professional help first.
Keywords: attachment theory; attachment anxiety; attachment avoidance; internal working models; Bayesian prior; demand–withdraw; pursuer–distancer; coupled dynamical systems; limit cycle; Gottman–Murray model; positivity ratio; Losada ratio; cross-validation; physiological linkage; co-regulation; attachment stability; earned security; repair attempts; Book of Changes; Mencius
目录 · Contents
- 序：两个人，一个回路English 中文Preface: Two People, One Loop
- 第一章 内部工作模型：从陌生情境到两个维度English 中文Chapter 1 Internal Working Models: From the Strange Situation to Two Dimensions
- 第二章 追—逃回路的耦合方程English 中文Chapter 2 Coupled Equations of the Pursue–Withdraw Loop
- 第三章 戈特曼与默里的婚姻方程English 中文Chapter 3 Gottman and Murray's Marriage Equations
- 第四章 冲突中的身体：生理联动与共调English 中文Chapter 4 The Body in Conflict: Physiological Linkage and Co-regulation
- 第五章 早期经验是宿命吗：纵向研究的真实效应量English 中文Chapter 5 Is Early Experience Destiny? The Real Effect Sizes of Longitudinal Studies
- 第六章 修复尝试：冲突回路中的阻尼器English 中文Chapter 6 Repair Attempts: The Damper in the Conflict Loop
- 第七章 原典并读：咸、家人、击鼓与反求诸己English 中文Chapter 7 Reading the Classics: *Xian*, *Jiaren*, "Beating the Drum" and Looking Within
- 第八章 实践与预注册试验English 中文Chapter 8 Practice and a Pre-registered Trial
How to cite · 引用
Fan, Y. (2026). Computational Attachment Theory and Couple Interaction Dynamics: From Anxious-Avoidant Coupled Oscillators and Gottman's Nonlinear Difference Equations to Updating Early Relational Priors [依恋理论的计算模型与伴侣互动动力学] (Version 1.0.0). 5D Library. https://doi.org/10.5281/zenodo.23754715
BibTeX
@book{fan2026attachment,
title = {{Computational Attachment Theory and Couple Interaction Dynamics}: From Anxious-Avoidant Coupled Oscillators and Gottman's Nonlinear Difference Equations to Updating Early Relational Priors},
author = {Fan, Yafu},
year = {2026},
publisher = {5D Library},
edition = {Version 1.0.0},
doi = {10.5281/zenodo.23754715},
url = {https://doi.org/10.5281/zenodo.23754715},
note = {Chinese title: 依恋理论的计算模型与伴侣互动动力学}
}
| DOI | https://doi.org/10.5281/zenodo.23754715 |
|---|---|
| DOI（全部版本 all versions） | https://doi.org/10.5281/zenodo.23754714 |
| ORCID | https://orcid.org/0009-0004-3519-1203 |
| 5D Library ID | 5DL-B-021 |
| 版本 Version | 1.0.0 · 中英双语版 Bilingual edition |
| 出版日期 Date | 2026-10-29 |
| 网址 Online | https://5dlibrary.com/books/attachment-couple-dynamics/ |
| SHA-256 · attachment-couple-dynamics_bilingual_v1.0.0.pdf | b2fc5a9b697b76e014d1d94dab7ca73bd7d0f16a8a5dc4ab66df63223b64f587 |
| SHA-256 · attachment-couple-dynamics_en_v1.0.0.pdf | 1fc4a14de424da4b6737e8e63dc508f35eabb7798a3d6e940288aab48c8eddbf |
| SHA-256 · attachment-couple-dynamics_zh_v1.0.0.pdf | d4b1311e7ccc688d52b424ecf65c607326afda2d9db2012a3960e89e166d8c82 |
| Licence · 许可 | Licensed under Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0). https://creativecommons.org/licenses/by-nc-nd/4.0/ |
Disclosure. The author uses the works of 5D Library, including this book, as the methodological basis of his community courses, the 5D Ascension Cards (Dimensional Shift Card Decks) and the Yafu AI knowledge base, and therefore has a commercial interest in the subject of this book. The book promotes no course, card deck or service; the Chapter 8 trial is designed to be run and analysed by researchers independent of the author's business and does not recruit from the author's community, students or customers; all the code and the study protocol are published openly for anyone to check.