The canard explosion is the change of amplitude and period of a limit cycle born in a Hopf bifurcation in a very narrow parameter interval. The phenomenon is well understood in singular perturbation problems where a small parameter controls the slow/fast dynamics. However, canard explosions are also observed in systems where no such parameter can obviously be identied. Here we show how the iterative method of Roussel and Fraser, devised to construct regular slow manifolds, can be used to determine a canard point in a general planar system of nonlinear ODEs. We demonstrate the method on the van der Pol equation, showing that the asymptotics of the method is correct, and on a templator model for a self-replicating system.
|Title of host publication||Proceedings of the 9th AIMS International Conference : Dynamical Systems and Differential Equations, DCDS Supplement 2013|
|Publisher||American Institute of Mathematical Sciences|
|Publication status||Published - 2013|
|Event||The 9th AIMS Conference on Dynamical Systems, Differential Equations and Applications - Orlando, FL, United States|
Duration: 1 Jul 2012 → 5 Jul 2012
|Conference||The 9th AIMS Conference on Dynamical Systems, Differential Equations and Applications|
|Period||01/07/2012 → 05/07/2012|