Dynamical Models of Dyadic Interactions with Time Delay

We will discuss a general class of linear models of dyadic interactions with a constant discrete time delay. In such models, changes of stability of stationary points occur for various intervals of parameters which determine the intensity of interactions. Conditions guaranteeing arbitrary number (that is zero, one or more) switches are formulated and the relevant theorems are proved. A systematic analysis of all generic cases is carried out. Possible generalizations to triadic interactions will also be presented. The talk is based on the joint work with U. Foryś and T. Płatkowski.