Bifurcation Analysis in Population Genetics Model with Partial Selfing
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 dyna...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/164504 |
| Summary: | 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. |
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| ISSN: | 1085-3375 1687-0409 |