Description of the emotional states of communicating people by mathematical model

The model we study is a generalization of the model considered by Liebovitch et al. (2008) and Rinaldi et al. (2010), and is related to the discrete model of the emotional state of communicating couples described by Gottman et al. (2002). Considered system of non-linear differential equations assumes that the emotional state of a person at any time is affected by the state of each actor alone, rate of return to that state, partner's emotional state and mutual sympathy. Interpreting the results, we focus on the analysis of the impact of a person's attitude to life (optimism or pessimism) on establishing emotional relations. It occurs that our conclusions are not always obvious from the psychological point of view.