Periodic and chaotic behaviour of a simple R&D model

The present paper deals with the dynamics of a simple descriptive non-linear R&D model. Special emphasis is put on the decision-making behaviour of real agents. Although our two-dimensional model is quite simple it produces periodic and chaotic behaviour. Despite we mainly concentrate on using numerical methods, we also present theoretical arguments for the occurrence of chaotic behaviour. We show that our time-discrete model can be reduced to a one-dimensional model by using a technique which is similar to the Poincaré section of ordinary differential equations. This one-dimensional model has the same dynamic properties. Since a majority of the theorems and results are in the context of dynamics in one dimension, we gain further insights by applying some interesting propositions.