University of Twente Student Theses
Homoclinic saddle to saddle-focus transitions in 4D systems
Kalia, Manu (2017) Homoclinic saddle to saddle-focus transitions in 4D systems.
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| Abstract: | We analyze a saddle to saddle-focus transition on a 4-dimensional homoclinic center manifold where the stable/unstable leading eigenspace is 3-dimensional (called the 3DL bifurcation). The transition is different from the Belyakov bifurcation, where a pair of complex eigenvalues split into two distinct real eigenvalues. Here a pair of complex eigenvalues and a real eigenvalue cross each other transversally, giving rise to a 3-dimensional stable/unstable leading situation. The work is motivated by the observation of this transition in [Meijer and Coombes, 2014] for the tame case (negative saddle quantity). We use near-to-saddle Poincare maps to give a detailed picture of global and local bifurcations occurring close to the critical saddle and the homoclinic connection respectively, in both wild and tame cases. We obtain sets of codimension 1 and 2 bifurcations that asymptotically approach the 3DL bifurcation point which are different in structure than those obtained in the Belyakov case. |
| Item Type: | Essay (Master) |
| Faculty: | EEMCS: Electrical Engineering, Mathematics and Computer Science |
| Subject: | 31 mathematics |
| Programme: | Applied Mathematics MSc (60348) |
| Link to this item: | https://purl.utwente.nl/essays/72956 |
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