Some remarks on the Gottman-Murray model of marital dissolution and time delays

Urszula Foryś

doi:10.3934/dcdsb.2018012

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2018, Volume 23, Issue 1: 181-191. Doi: 10.3934/dcdsb.2018012

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Some remarks on the Gottman-Murray model of marital dissolution and time delays

Urszula Foryś

Institute of Applied Mathematics and Mechanics, Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Banacha 2, 02-097 Warsaw, Poland

Received: November 2016

Published: November 2017

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Abstract

In the paper we consider mathematical model proposed by Gottman, Murray and collaborators to describe marital dissolution. This model is described in the framework of discrete dynamical system reflecting emotional states of wife and husband during consecutive rounds of talks between spouses. The model is, however, non-symmetric. To make it symmetric, one need to assume that the husband reacts with delay. Following this idea we consider the influence of time delays in the reaction terms of wife or/and husband. The delay means that one or both of spouses split their attention between present and previous rounds of talks. We study possibility of the change of stability with increasing delay. Surprisingly, it occurs that the delay has no impact on the stability, that is the condition of stability proposed by Murray remains unchanged.

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Mathematics Subject Classification: Primary: 91D99; Secondary: 37C75, 37N99.

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