Dynamical Models of Dyadic Interactions with Delay

Abstract

We investigate a general class of linear models of dyadic interactions with a constant discrete time delay. We prove that the changes in stability of the stationary states occur for various intervals of the parameters that determine the strength and nature of emotional interactions between the partners. The dynamics of interactions depend on both reactivity of partners to their own emotional states as well as to the partner's states. The results suggest that reactivity to the partner's states has greater impact on the dynamics of the relationship than the reactivity to one's own states. Moreover, the results underscore the importance of deliberation in maintaining the stability of the relationship. Moreover, we have found that multiple stability switches are only possible when one of the partners reacts with delay to their own emotional states. We also propose a generalization to triadic interactions.

Keywords:

• discrete delay
• dyadic interactions
• stability switches

Acknowledgments

The article was supported by the Polish Government Grant no. N N201 362536. The authors thank Dr. Marek Bodnar and the anonymous Referees for their helpful remarks and suggestions.