Working paper sustainability and innovation S12/2011
The diffusion of innovations is an important process and its models have applications in many fields, with particular relevance in technological forecast. The logistic equation is one of most important models in this context. Extensions of this approach as the Lotka-Volterra model have been developed to include the effect of mutual influences between technologies such as competition. However, many of the parameters entering this description are uncertain, difficult to estimate or simply unknown, particularly at early stages of the diffusion. Here, a systematic way to study the effect of uncertain or unknown parameters on the future diffusion of interacting innovations is proposed. The input required is a general qualitative understanding of the system: is the mutual influence positive or negative and does it apply symmetrically to either technology? Since the parameters enter the problem via a set of coupled non-linear differential equations, the approach proposed here goes beyond simple Monte-Carlo-like methods where the result is an explicit function of the parameters. The methodology is developed in detail and applied the case of three types of upcoming electric vehicle propulsion technologies. The findings indicate that competition between electric vehicles and mild hybrid vehicles implies a slow decline of the latter. The approach can easily be generalised to include other initial conditions, more technologies or other technological areas to find stable results for future market evolution independent of specific parameters.
diffusion of innovations logistic equation competition electric vehicles Monte Carlo methods