Open Access
2013 Bifurcation Analysis in Population Genetics Model with Partial Selfing
Yingying Jiang, Wendi Wang
Abstr. Appl. Anal. 2013: 1-9 (2013). DOI: 10.1155/2013/164504


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.


Download Citation

Yingying Jiang. Wendi Wang. "Bifurcation Analysis in Population Genetics Model with Partial Selfing." Abstr. Appl. Anal. 2013 1 - 9, 2013.


Published: 2013
First available in Project Euclid: 27 February 2014

zbMATH: 1383.37072
MathSciNet: MR3035390
Digital Object Identifier: 10.1155/2013/164504

Rights: Copyright © 2013 Hindawi

Vol.2013 • 2013
Back to Top