Abstract
Motivated by a problem from pharmacology, we consider a general two parameter slow–fast system in which the critical set consists of a one dimensional manifold and a two dimensional manifold, intersecting transversally at the origin. Using geometric desingularisation, we show that for a subset of the parameter set there is an exchange of stabilities between the attracting components of the critical set and the direction of the continuation can be expressed in terms of the parameters.
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References
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Acknowledgements
CG was supported in this work by the EPSRC Doctoral Training Grant 1363360. GD thanks the Centre de Recerca Matemàtica for the opportunity to discuss the work with other participants in the Intensive Research Program on Advances in Nonsmooth Dynamics.
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Gavin, C., Aston, P.J., Derks, G. (2017). Extending Slow Manifolds Near a Degenerate Transcritical Intersection in Three Dimensions. In: Colombo, A., Jeffrey, M., Lázaro, J., Olm, J. (eds) Extended Abstracts Spring 2016. Trends in Mathematics(), vol 8. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-55642-0_12
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DOI: https://doi.org/10.1007/978-3-319-55642-0_12
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