We study a dynamic model of the relationship between two people where the states depend on the "power" in the relationship. We perform a comprehensive analysis of stability of the system, and determine a set of conditions under which stable relationships are possible. In particular, stable relationships can occur if both people are dominant, but the sum of dominances is below a bound determined by the model's parameters. Stable relationships can also occur if one person is dominant and the other is submissive, provided the level of dominance exceeds the level of submissiveness but not beyond a threshold. We also conclude that a stable relationship is not possible if both people are submissive. While our model is motivated by a social or romantic relationship, it can also be applied to professional or business relationships as well as diplomatic relationships between nations.
翻译：我们研究两个民族之间的关系动态模式,即国家依赖于关系中的“权力”。我们全面分析体系的稳定性,确定一系列稳定关系可以实现的条件。特别是,如果双方都是主导者,但支配地位的总和低于模式参数所确定的约束,稳定关系可以实现。如果一个人是主导者,而另一个人是顺从者,则稳定关系也可以实现,条件是支配地位的程度超过顺从程度,但不超过门槛。 我们还得出结论,如果双方都是顺从者,稳定关系是不可能的。 虽然我们的模式是由社会或浪漫关系驱动的,但它也可以适用于职业或商业关系以及国家间的外交关系。
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