Extending slow manifolds near transcritical and pitchfork singularities

By Martin Krupa, Peter Szmolyan. 2001

178 citations recorded by the source corpus.

Subfields: Computer Networks and Communications, Molecular Biology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f94dc493b5ebb86927e5a91a2ae7da5af5cc75fc

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computer Networks and Communications

1. John M. Guckenheimer
2. Hinke M. Osinga
3. Martin Wechselberger
4. Bernd Krauskopf
5. Mathieu Desroches
6. Bjorn Sandstede
7. Ale Jan Homburg
8. Christian Kuehn

In Molecular Biology

1. Bjorn Sandstede
2. Christian Kuehn

In Statistical and Nonlinear Physics

1. John M. Guckenheimer
2. Christian Kuehn
3. Hinke M. Osinga
4. Martin Wechselberger
5. Bernd Krauskopf
6. Mathieu Desroches
7. Bjorn Sandstede
8. Ale Jan Homburg

Citations in the corpus

• A mathematical framework for critical transitions: Bifurcations, fast–slow systems and stochastic dynamics (2011, background): “Pitchfork and transcritical transitions are treated in [49].”
• Homoclinic and heteroclinic bifurcations in vector fields (2010, background): “If M0 is not normally hyperbolic, then geometric blowup can often be used to analyze the dynamics, and [120, 241] contain recent results in this direction.”
• Mixed-Mode Oscillations with Multiple Time Scales (2012, background): “We remark that S may have singularities [141], but we assume here that this does not happen so that S is a smooth manifold.”