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.
Citation: Xinying Liu. Stochastic modeling of intimacy-conflict dynamics in non-traditional stable marriages[J]. Electronic Research Archive, 2026, 34(1): 376-410. doi: 10.3934/era.2026018
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.
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Xinying Liu. Stochastic modeling of intimacy-conflict dynamics in non-traditional stable marriages[J]. Electronic Research Archive, 2026, 34(1): 376-410. doi: 10.3934/era.2026018
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