Bifurcation analysis of a nonlinear field model of regeneration |
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| Authors: | Ding da-fu John Totafurno L. E. H. Trainor |
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| Affiliation: | (1) Physics Department, University of Toronto, M5S 1A7 Toronto, Canada;(2) Anatomy Department, Faculty of Medicine, University of Toronto, M5S IA8 Toronto, Canada;(3) Departments of Physics and Medicine, University of Toronto, M5S 1A7 Toronto, Canada;(4) Present address: Shanghai Institute of Biochemistry, Chinese Academy of Sciences, 20031 Shanghai, China |
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| Abstract: | The analysis of bifurcating solutions in the Totafurno and Trainor [23] model of supernumerary limb production in salamanders is re-examined using the symmetry analysis developed by Totafurno [22]. In particular, we show analytically that the appearance of field solutions possessing 2 and 4 singularities (the 2- and 4-centered solutions, respectively) also correspond to true bifurcations with reduced symmetries, just as had been previously found for a solution to the field equations not possessing such singularities (the twist solution). While the results have significance primarily for the biological problem, this work serves as an instructive example of the application of symmetry groups to the bifurcation analysis of nonlinear field equations arising from a variational principle. The relationship between the solutions of the nonlinear equations and the corresponding linear equations is discussed.Supported by the National Sciences and Engineering Research Council and the Medical Research Council of CanadaTo whom correspondence should be sent |
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| Keywords: | Bifurcation analysis Symmetry-breaking Nonlinear models Limb regeneration |
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