Glendinning, Paul (2015) Classification of Boundary Equilibrium Bifurcations in planar Filippov systems. [MIMS Preprint]
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Abstract
If a family of piecewise smooth systems depending on a real parameter is defined on two different regions of the plane separated by a switching surface then a boundary equilibrium bifurcation occurs if a stationary point of one of the systems intersects the switching surface at a critical value of the parameter. We derive the leading order terms of a normal form for boundary equilibrium bifurcations of planar systems. This makes it straightforward to derive a complete classification of the bifurcations that can occur. We are thus able to confirm classic results of Filippov\cite{Fil} using different and more transparent methods, and explain why the `missing' cases of Hogan \emph{et al}\cite{Hog} are the only cases omitted in more recent work.
| Item Type: | MIMS Preprint |
|---|---|
| Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 34 Ordinary differential equations MSC 2010, the AMS's Mathematics Subject Classification > 37 Dynamical systems and ergodic theory |
| Depositing User: | Professor Paul Glendinning |
| Date Deposited: | 01 Jul 2015 |
| Last Modified: | 08 Nov 2017 18:18 |
| URI: | https://eprints.maths.manchester.ac.uk/id/eprint/2327 |
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