Chaotic Aspects of a GRM1 Innovation Diffusion Model Christos H. Skiadas 1 , Giannis Rompogiannakis 1 , Apostolos Apostolou 2 , and John Dimotikalis 2 1 Technical University of Crete Department of Production Engineering and Management, Data Analysis and Forecasting Laboratory, 73100 Chania, Crete, Greece (e-mail: skiadas@ermes.tuc.gr) 2 Technological Educational Institute of Crete Heraclion, Crete, Greece Abstract. Chaotic behavior of a generalized rational (GRM1) innovation diffusion model is studied. The deterministic continuous version of this model was proposed, analyzed and applied in earlier publications. Here, the chaotic behavior is expressed through the discrete alternative of the continuous GRM1 model. The model shows symmetric and non-symmetric behavior expressed by a parameter σ. In this ar- ticle it is found that when the diffusion parameter b and the parameter σ verify the relation b/σ ≥ 2 then the chaotic aspects of the model appear. A method is proposed for fitting the model to the data. Time series data expressing the cumu- lative percentage of steel produced by the oxygen process in various countries are used. Characteristic graphs of the chaotic behavior are given and applications are presented. Keywords: Chaotic modeling, Diffusion modeling, Speed of diffusion, Innovation diffusion, Non-linear models, Chaotic oscillations. 1 Introduction It’s become a commonplace to call this the information age, but an even more appropriate name might be the information age. In 1997, for example, the U.S. Patent and Trademark Office received 237.000 patent applications, a 15% increase from the year before. Also in 1997, the agency granted 124.127 patents, a record number and an increase of 16% from the volume it recorded at the beginning of the decade in 1991, a year that had also set a record for patent activity. At individual companies, the pace of innovation is even greater. In 1998, IBM Corp. received 2.657 patents for inventions, an in- crease of 54% from the number it won in 1997, according to a preliminary tally from the patent office. This was not a one-time surge, as IBM has been the leading recipient of U.S. patents for six consecutive years. And IBM was not alone in recording huge increases in U.S. patent activity last year: Sony Corp.’s patent number rose 53%, Eastman Kodak Co.’s 41%, and Motorola Inc.’s 33%, [Maguire and Hagen, 2001]. While not all patents translate into