WIAS Preprint No. 872, (2003)

On immediate-delayed exchange of stabilities and periodic forced canards


  • Schneider, Klaus R.
  • Nefedov, Nikolai N.

2010 Mathematics Subject Classification

  • 34E15 34E05 34C25


  • exchange of stabilities, periodic forced canards, singularly perturbed ordinary differential equations




We study scalar singularly perturbed non-autonomous ordinary differential equations whose associated equations feature the property of exchange of stabilities, i.e., the set of their equilibria consists of at least two intersecting curves. By means of the method of asymptotic lower and upper solutions we derive conditions guaranteeing that the solution of initial value problems exhibit the phenomenon of immediate exchange of stabilities as well as the phenomenon of delayed exchange of stabilities. We use this result to prove the existence of forced canard solutions.

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