Mathieu Desroches

Preprints

• Mixed-mode oscillations due to a singular Hopf bifurcation in a forest pest model.    arXiv 
  M. Brøns, M. Desroches and M. Krupa
  

• Numerical continuation techniques for planar slow-fast systems.    arXiv 
  P. De Maesschalck and M. Desroches
  

• Mixed-mode oscillations in a multiple time scale phantom bursting system.    arXiv 
  M. Krupa, A. Vidal, M. Desroches and F. Clément
  

• On the numerical continuation of isolas of equilibria.    arXiv 
  D. Avitabile, M. Desroches and S. Rodrigues

• Spike-adding and codimension-two homoclinic bifurcations in the Hindmarsh-Rose burster.    arXiv 
  D. Linaro, A. R. Champneys, M. Desroches and M. Storace
  

• Canards, inflection and excitability threshold in neuronal models.    arXiv 
  M. Desroches, M. Krupa and S. Rodrigues
  

Peer-reviewed journal articles

10. Mixed-mode oscillations with multiple time scales, SIAM Review 54(2): 211-288, 2012.
    M. Desroches, J. Guckenheimer, B. Krauskopf, C. Kuehn, H. M. Osinga and M. Wechselberger    preprint  
9. Canards of mixed type in a neural burster, Physical Review E 85(2): 021920, 2012.    arXiv 
   M. Desroches, J. Burke, T. J. Kaper and M. A. Kramer
   
8. A showcase of torus canards in neuronal bursters, The Journal of Mathematical Neuroscience 2: 3, 2012.    arXiv 
   J. Burke, M. Desroches, A. M. Barry, T. J. Kaper and M. A. Kramer
   
7. Canard and curvature: the “ smallness of ε ” in slow-fast dynamics, Proceedings of the Royal Society A 467(2132): 2404-2421, 2011.
   M. Desroches and M. R. Jeffrey    preprint  
6. Canard and curvature: nonsmooth approximation by pinching, Nonlinearity 24(5): 1655-1682, 2011.
   M. Desroches and M. R. Jeffrey   preprint  
5. Canard cycles in aircraft ground dynamics, Nonlinear Dynamics 66(4): 681-688, 2011.
   J. Rankin, M. Desroches, B. Krauskopf and M. Lowenberg   preprint  
4. Numerical continuation of canard orbits in slow-fast dynamical systems, Nonlinearity 23(3): 739-765, 2010.
   M. Desroches, B. Krauskopf and H. M. Osinga   preprint  
3. The geometry of mixed-mode oscillations in the Olsen model for the Peroxidase-Oxidase reaction, Discrete and Continuous Dynamical Systems - Series S 2(4): 807-827, 2009. M. Desroches, B. Krauskopf and H. M. Osinga   preprint  
2. The geometry of slow manifolds near a folded node, SIAM Journal on Applied Dynamical Systems 7(4): 1131-1162, 2008.
   M. Desroches, B. Krauskopf and H. M. Osinga   preprint  
1. Mixed-mode oscillations and slow manifolds in the self-coupled FitzHugh-Nagumo system, Chaos 18(1): 015107, 2008.
   M. Desroches, B. Krauskopf and H. M. Osinga   preprint  

Conference proceedings

• Numerical continuation of isolas of equilibria, 7th European Nonlinear Oscillations Conference (ENOC), Rome (Italy), July 2011.
  D. Avitabile, M. Desroches and S. Rodrigues

• Numerical continuation of canard-like orbits in piecewise-linear dynamical systems, 7th European Nonlinear Oscillations Conference (ENOC), Rome (Italy), July 2011.
  P. Thota and M. Desroches

Work in progress

• Shil'nikov chaos in a synaptic model for working memory, in preparation, 2012.
  J. M. Cortes, M. Desroches and S. Rodrigues
  

• Canards under the miscroscope, in preparation, 2012.
  M. Desroches and M. Jeffrey