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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 164504, 9 pages
http://dx.doi.org/10.1155/2013/164504
Research Article

Bifurcation Analysis in Population Genetics Model with Partial Selfing

1School of Science, Sichuan University of Science & Engineering, Zigong, Sichuan 643000, China
2School of Mathematics and Statistics, Southwest University, Chongqing 400715, China

Received 23 October 2012; Revised 4 February 2013; Accepted 7 February 2013

Academic Editor: Ljubisa Kocinac

Copyright © 2013 Yingying Jiang and Wendi Wang. 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

A new model which allows both the effect of partial selfing selection and an exponential function of the expected payoff is considered. This combines ideas from genetics and evolutionary game theory. The aim of this work is to study the effects of partial selfing selection on the discrete dynamics of population evolution. It is shown that the system undergoes period doubling bifurcation, saddle-node bifurcation, and Neimark-Sacker bifurcation by using center manifold theorem and bifurcation theory. Numerical simulations are presented not only to illustrate our results with the theoretical analysis, but also to exhibit the complex dynamical behaviors, such as the period-3, 6 orbits, cascade of period-doubling bifurcation in period-2, 4, 8, and the chaotic sets. These results reveal richer dynamics of the discrete model compared with the model in Tao et al., 1999. The analysis and results in this paper are interesting in mathematics and biology.