@article{Liu2026, 
author = {Xinying Liu},
title = {Stochastic modeling of intimacy-conflict dynamics in non-traditional stable marriages},
year = {2026},
journal = {Electronic Research Archive},
volume = {34},
number = {1},
pages = {376-410},
keywords = {marital relationship mode, stochastic differential equations, stochastic stability, sensitivity analysis},
url = {https://www.sciopen.com/article/10.3934/era.2026018},
doi = {10.3934/era.2026018},
abstract = {Most prior couple dynamics research has focused on either high-conflict, low-stability relationships or low-conflict, high-stability relationships, relying predominantly on deterministic models. We investigate the stability of the far-less-studied dynamically balanced regime characterized by recurrent small conflicts, occasional large conflicts, and spontaneous repair processes in an intrinsically stochastic environment. An intimacy–conflict model couples dual stochasticity: event timing follows independent Poisson processes, and impact magnitudes follow uniform distributions. Formal proofs establish the existence and uniqueness of solutions, bounded states within    [  0  ,  1  ], stochastic stability of intimacy around its baseline, and convergence to a unique stationary distribution. Simulations show that intimacy drifts back to its usual level, that the impact of each event depends on the couple's current state, and that built-in repair keeps the system steady while mirroring real-life ups and downs. The study extends theory on conflict–intimacy coevolution and provides a framework for marital research and intervention.}
}