# American Institute of Mathematical Sciences

December  2014, 19(10): 3299-3317. doi: 10.3934/dcdsb.2014.19.3299

## The dynamics of technological change under constraints: Adopters and resources

 1 Departamento de Matemáticas Aplicadas y Sistemas, DMAS, Universidad Autónoma Metropolitana, Cuajimalpa, Av. Vasco de Quiroga 4871, Col. Santa Fe Cuajimalpa, Cuajimalpa de Morelos, 05300, México, D.F., Mexico 2 Instituto de Matemáticas, Universidad Nacional Autónoma de México, Boulevard Juriquilla No. 3001, Juriquilla, 76230, Mexico 3 Departamento de Ecología, Facultad de Ciencias Biológicas, Pontificia Universidad Católica de Chile, Casilla 114-D, Santiago 6513677, Chile

Received  July 2013 Revised  April 2014 Published  October 2014

We present a mathematical model for a technology cycle that centers its attention on the coexistence mechanisms of competing technologies. We use a biological analogy to couple the adoption of a technology with the provision of financial resources. In our model financial resources are limited and provided at a constant rate. There are two variants analyzed in this work, the first considers the so-called internal innovation and the second introduces external innovation. We make use of the adaptive dynamics framework to explain the persistence of closely related technologies as opposed to the usual competitive exclusion of all but one dominant technology. For internal innovation the existence of a resource remanent in the full adoption case does not always lead to competitive exclusion; otherwise with the external innovation the resident technology can not be displaced. The paper illustrates the persistence of closely related technologies and the competitive exclusion in renewable energy technologies and TV sets respectively.
Citation: M. Núñez-López, J. X. Velasco-Hernández, P. A. Marquet. The dynamics of technological change under constraints: Adopters and resources. Discrete & Continuous Dynamical Systems - B, 2014, 19 (10) : 3299-3317. doi: 10.3934/dcdsb.2014.19.3299
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