Bifurcation of extremals in the analysis of bifurcation Solutions of Duffing equation | ||
| Journal of College of Education for Pure Science | ||
| Article 1, Volume 2, Issue 4, December 2012, Pages 73-92 | ||
| Authors | ||
| Mudhir A. Abdul Hussain; Hussein K. Kadhim | ||
| Abstract | ||
| In the present paper we are interested in the study of bifurcation of extremals of smooth functions. We considered the functions that have codimensions three (hyperbolic umbilic) and fifteen at the origin. For the function of codimension three we gave the conditions of the existence of the critical points. Also, we found the bif-spreading of the critical points. For the function of codimension fifteen we used the boundary singularities of smooth maps to study the bifurcation analysis of this function, also we found geometrical description of the caustic. | ||
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