Entrainment of modulation frequency: A case study
- Recke, Lutz
- Schneider, Klaus R.
2010 Mathematics Subject Classification
- 34E10 34C14 34C27 34C29 34C30 34C25
- frequency entrainment, modulated wave, equivariance, approximate synchronization
We consider a system of autonomous ODE's which is $S^1$-equivariant and has a family of asymptotically stable modulated wave solutions with wave frequency $alpha_0$ and modulation frequency $beta_0$. This system will be perturbed, where the applied nonautonomous force also represents a modulated wave, but with wave frequency $alpha$ and modulations frequency $beta$. The strength of this perturbation is not necessarily small. Our goal is to look for conditions such that the perturbed system exhibits an approximate entrainment of the modulation frequency $beta$ on any given finite time interval, where the approximation error can be controlled by the wave frequency.