Authors
Abstract
In this paper, we study the numerical analysis of fold-pitchfork bifurcation with Z2 symmetry. For this purpose, explicit formulas for the critical coefficients of this bifurcation are obtained and non-degeneracy conditions of this bifurcation are determined. Then, local bifurcations, bifurcation curves and phase portraits are computed by MatCont toolbox. We will emphasize an example serving as a model of pipe flow
Keywords
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15. W Govarets, “Numerical Methods for Bifurcations of Dynamical Equilibria”, SIAM (2000).
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2. H A Dijkstra et al., Commun. Comput. Phys. 15 (2014) 1.
3. J D Crawford and E Knobloch, Annu. Rev. Fluid Mech. 23 (1991) 341.
4. F Marques, F Mellibovsky, and A Meseguer, Physical Review E 88 (2013) 013006.
5. F Mellibovski and B Eckhardt, J. Fluid Mechanics 709 (2012) 149.
6. H Meijer, “Codimension 2 Bifurcations of Iterated Maps”,Utrecht University. (2006).
7. Kuznetsov, “Elements of Applied Bifurcation Theory”, Springer-Verlag, Berline. (1998)
8. Y Kuznetsov, H Meijer, and L V Veen, Internat. J. Bifur. Chaos Appl. Sci. Engrg. 7 (2004) 2253.
9. Y Kuznetsov and H Meijer, SIAM. J. Sci. Comput. 26 (2005) 1932.
10. W Govarets, R Khoshsiar Ghaziani, Y Kuznetsov, and H Meijer, SIAM. J. Sci. Comput. 29 (2007) 2644.
11. E J Doedel, B E Oldeman, A R Champneys, F Dercole, T F Fairgrieve, Y Kuznetsov, R C Paffenroth, B Sandsted, X J Wang and C H Zhang, AUTO-07p, “Continuation and Bifurcation Software for Ordinary Differential Equations”, Concordia University, Version 0.9.1, (2012).
12. A Dhooge, W Govaerts, Yu A Kuznetsov, H G E Meijer and B Sautois, Math. Com. Mod. Dyn. Systems. 14 (2008) 147.
13. R Mazrooei-Sebdani, Z Eskandari and H G E Meijer, Department of Mathematics, University of Twente, (2017) TW memoramdum 2058.
14. M Golubitkky, I Stewart, and D G Schaeffer, “Singularities and Groups in Bifurcation Theory”, Springer-Verlag, Berline. (1980).
15. W Govarets, “Numerical Methods for Bifurcations of Dynamical Equilibria”, SIAM (2000).
16. M R Sarkardei, Iranian Journal of Physics Research, 2, 5 (2001) 74.
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