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Bifurcation Analysis in Population Genetics Model with Partial Selfing.

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Title: Bifurcation Analysis in Population Genetics Model with Partial Selfing.
Authors: Yingying Jiang1 jyy@suse.edu.cn, Wendi Wang2
Source: Abstract & Applied Analysis. 2013, p1-9. 9p.
Subjects: Population genetics -- Mathematical models, Bifurcation theory, Discrete systems, Computer simulation, Comparative studies
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. [ABSTRACT FROM AUTHOR]
Copyright of Abstract & Applied Analysis is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Bifurcation Analysis in Population Genetics Model with Partial Selfing.
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  Data: <searchLink fieldCode="AR" term="%22Yingying+Jiang%22">Yingying Jiang</searchLink><relatesTo>1</relatesTo><i> jyy@suse.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Wendi+Wang%22">Wendi Wang</searchLink><relatesTo>2</relatesTo>
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  Data: <searchLink fieldCode="JN" term="%22Abstract+%26+Applied+Analysis%22">Abstract & Applied Analysis</searchLink>. 2013, p1-9. 9p.
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  Data: <searchLink fieldCode="DE" term="%22Population+genetics+--+Mathematical+models%22">Population genetics -- Mathematical models</searchLink><br /><searchLink fieldCode="DE" term="%22Bifurcation+theory%22">Bifurcation theory</searchLink><br /><searchLink fieldCode="DE" term="%22Discrete+systems%22">Discrete systems</searchLink><br /><searchLink fieldCode="DE" term="%22Computer+simulation%22">Computer simulation</searchLink><br /><searchLink fieldCode="DE" term="%22Comparative+studies%22">Comparative studies</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: 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. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Abstract & Applied Analysis is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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      – Type: doi
        Value: 10.1155/2013/164504
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 9
        StartPage: 1
    Subjects:
      – SubjectFull: Population genetics -- Mathematical models
        Type: general
      – SubjectFull: Bifurcation theory
        Type: general
      – SubjectFull: Discrete systems
        Type: general
      – SubjectFull: Computer simulation
        Type: general
      – SubjectFull: Comparative studies
        Type: general
    Titles:
      – TitleFull: Bifurcation Analysis in Population Genetics Model with Partial Selfing.
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          Name:
            NameFull: Yingying Jiang
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          Name:
            NameFull: Wendi Wang
    IsPartOfRelationships:
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          Dates:
            – D: 01
              M: 01
              Text: 2013
              Type: published
              Y: 2013
          Identifiers:
            – Type: issn-print
              Value: 10853375
          Titles:
            – TitleFull: Abstract & Applied Analysis
              Type: main
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