Department of Mathematics
 Search | Help | Login | pdf version | printable version

Math @ Duke





.......................

.......................


Publications [#20941] of W Garrett Mitchener

Papers Published

  1. W.G. Mitchener and Martin A. Nowak, Chaos and Language, Proceedings of the Royal Society: Biological Sciences, vol. 271 no. 1540 (April, 2004), pp. 701--704 [2643]
    (last updated on 2004/03/30)

    Author's Comments:
    This paper covers material from part of one chapter of my dissertation.

    Abstract:
    Human language is a complex communication system with unlimited expressibility. Children spontaneously develop a native language by exposure to linguistic data from their speech community. Over historical time, languages change dramatically and unpredictably by accumulation of small changes and by interaction with other languages. We have previously developed a mathematical model for the acquisition and evolution of language in heterogeneous populations of speakers. This model is based on game dynamical equations with learning. Here we show that simple examples of such equations can display complex limit cycles and chaos. Hence, language dynamical equations mimic complicated and unpredictable changes of languages over time. In terms of evolutionary game theory, we note that imperfect learning can induce chaotic switching among strict Nash equilibria.

 

dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320