Instability and chaotic behaviour in a discrete dynamic producer–consumer model by Molnár and Szidarovszky

The present paper analyses the behaviour of a discrete dynamic producer–consumer model defined by Molnár and Szidarovszky, and focuses on the unstable region of the adaptive and the extrapolative model versions, assuming that the market price changes proportionally to the level of disequilibrium, that is, the difference between the demanded and the supplied product amount. A lower limit was attached to the market price in the model, namely, the price was limited to nonnegative values. Due to this limit the model structure becomes nonlinear instead of the original linear structure. This simple structure generates very complicated behaviour, including chaotic behaviour, and shows great sensitivity to the parameter value K, which is the coefficient associated with the supply–demand difference in the price formation.