Diffusion paths: fixed points, periodicity and chaos

Abstract

It is common to recognize that ideas, technology and information disseminate across the economy following some kind of diffusion pattern. Typically, the process of adopting a new piece of knowledge will be translated into an s-shaped trajectory for the adoption rate. This type of process of diffusion tends to be stable in the sense that convergence from any initial state towards the long-term scenario in which all the potential adopters enter in contact with the innovation is commonly guaranteed. Here, we introduce a mechanism under which stability of the diffusion process does not necessarily hold. When the perceived law of motion concerning the evolution of the number of potential adopters differs from the actual law of motion, and agents try to learn this law resorting to an adaptive learning rule, nonlinear long-term outcomes might emerge: the percentage of individuals accepting the innovation in the long-run may be a varying value that evolves according to some cyclical (periodic or a-periodic) pattern. The concept of nonlinear diffusion that is addressed is applied to a problem of information and monetary policy.