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Time delays in dyadic interactions on the example of relations between optimists and pessimists

In this paper, a delayed model of interactions between two actors in the context of their internal optimism and pessimism is studied. Considered model is based on the model proposed earlier in the context of romantic relationships. With the use of the system of nonlinear delay differential equations, we describe the change of emotions of two actors. Delays in the inertial component and in the influence function are introduced, and their influence on the system dynamics is investigated focusing on most beneficial meetings for actors. Finally, the modified systems are compared with the nondelayed case, and results are illustrated by numerical solutions for particular investigated scenarios.