Bifurcation Analysis in Population Genetics Model with Partial Selfing

A new model which allows both the effect ofpartial 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 usingcenter manifold theorem and bifurcation theory. Numericalsimulations are presented not only to illustrate our results withthe theoretical analysis, but also to exhibit the complexdynamical behaviors, such as the period-3, 6 orbits, cascade ofperiod-doubling bifurcation in period-2, 4, 8, and the chaoticsets. These results reveal richer dynamics of the discrete modelcompared with the model in Tao et al., 1999. The analysis and results inthis paper are interesting in mathematics and biology