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...
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Series: | Abstract and Applied Analysis |
Online Access: | http://dx.doi.org/10.1155/2013/164504 |
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doaj-83c5c93cd21a413f98bc5e05a17c5e102020-11-25T00:32:52ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/164504164504Bifurcation Analysis in Population Genetics Model with Partial SelfingYingying Jiang0Wendi Wang1School of Science, Sichuan University of Science & Engineering, Zigong, Sichuan 643000, ChinaSchool of Mathematics and Statistics, Southwest University, Chongqing 400715, ChinaA 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.http://dx.doi.org/10.1155/2013/164504 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Yingying Jiang Wendi Wang |
spellingShingle |
Yingying Jiang Wendi Wang Bifurcation Analysis in Population Genetics Model with Partial Selfing Abstract and Applied Analysis |
author_facet |
Yingying Jiang Wendi Wang |
author_sort |
Yingying Jiang |
title |
Bifurcation Analysis in Population Genetics Model with Partial Selfing |
title_short |
Bifurcation Analysis in Population Genetics Model with Partial Selfing |
title_full |
Bifurcation Analysis in Population Genetics Model with Partial Selfing |
title_fullStr |
Bifurcation Analysis in Population Genetics Model with Partial Selfing |
title_full_unstemmed |
Bifurcation Analysis in Population Genetics Model with Partial Selfing |
title_sort |
bifurcation analysis in population genetics model with partial selfing |
publisher |
Hindawi Limited |
series |
Abstract and Applied Analysis |
issn |
1085-3375 1687-0409 |
publishDate |
2013-01-01 |
description |
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. |
url |
http://dx.doi.org/10.1155/2013/164504 |
work_keys_str_mv |
AT yingyingjiang bifurcationanalysisinpopulationgeneticsmodelwithpartialselfing AT wendiwang bifurcationanalysisinpopulationgeneticsmodelwithpartialselfing |
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1725318665248702464 |