Complex dynamics in a threshold advertising model

During the last decade economic models of varying complexity have been studied by using the qualitative theory of nonlinear dynamical systems theory. The purpose of the present paper is to analyze an economic model which is as simple as possible but exhibits sufficient nonlinearity to admit chaotic orbits. A firm's market share is assumed to be influenced only by a simple threshold advertising rule. It turns out that such a simple rule may create complex behavioural patterns, i.e., periodic orbits of any length and even chaotic, seemingly unpredictable time paths. By using the package LOCBIF we are able to investigate for which model parameters chaos arises and how the transition from stable equilibrium to chaos occurs.This work has been financially supported by the Austrian Science Foundation, project No. 7783-PHY.