ИСТИНА

А rather general mathematical model describing the interaction between two actors is considered. The actors may be various social subjects, ranging from individuals and social groups to states and nations.: social or political groups, economic agents, individuals, states, nations, etc. The model is based on a system of two nonlinear ordinary differential equations. It is sufficiently simple (not more complex that the well-known predator–prey system or the two-species competition model). The model is an extension of the Murray–Gottman model originally proposed to investigate marital interaction. The phase variables describing the actor states may be positive or negative, unlike biological models where the size of the interacting populations is always positive. Positive states are associated with feelings of satisfaction, friendship, or cooperation, whereas negative states signal dissatisfaction, unfriendliness, or enmity. Moving over the scale of states from negative to positive values, we obtain various degrees of bad or good relations between the partners. In this model, collaboration is represented as positive feedback between the actors, i.e., a positive state of one actor boosts the positive state of the other actor, whereas a negative state of one actor amplifies the other actor’s negative state. Competition is modeled as negative feedback, when a positive state of one actor amplifies the negative state of the other actor, whereas a negative state of one actor amplifies the positive state of the other (in other words, what is worse for one is better for the other). The system dynamics for excitable, self-sufficient, and some other types of actors who, in the absence of a partner, do not strive to a neutral state, as in the Murray–Gottman model was studied. New functions are investigated describing the mutual influence of the partners. In particular, the influence function depends not only on the states of the partners, but also on their own states. New types of dynamic behavior are discovered. In particular, the model in some cases displays oscillatory dynamics, which has not been observed in earlier models. The model has a rich set of phase portraits describing the interaction dynamics between two actors and can be applied to model various socio-economic interrelationships between two partners.