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The Scientific World Journal
Volume 2014, Article ID 835069, 11 pages
http://dx.doi.org/10.1155/2014/835069
Research Article

Mutation and Chaos in Nonlinear Models of Heredity

Department of Computational & Theoretical Sciences, Faculty of Sciences, International Islamic University Malaysia, P.O. Box 141, 25710 Kuantan, Pahang, Malaysia

Received 31 March 2014; Accepted 30 June 2014; Published 21 July 2014

Academic Editor: Mujahid Abbas

Copyright © 2014 Nasir Ganikhodjaev et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We shall explore a nonlinear discrete dynamical system that naturally occurs in population systems to describe a transmission of a trait from parents to their offspring. We consider a Mendelian inheritance for a single gene with three alleles and assume that to form a new generation, each gene has a possibility to mutate, that is, to change into a gene of the other kind. We investigate the derived models and observe chaotic behaviors of such models.