Robust heteroclinic cycles occur naturally in many classes of nonlinear differential equations with invariant hyperplanes. In particular they occur frequently in models for ecological dynamics and fluid mechanical instabilities. We consider the effect of small-amplitude time-periodic forcing and describe how to reduce the dynamics to a two-dimensional map. In the limit where the heteroclinic cycle loses asymptotic stability, intervals of frequency locking appear. In the opposite limit, where the heteroclinic cycle becomes strongly stable, the dynamics remains chaotic and no frequency locking is observed.
|Journal||Physical Review E - Statistical, Nonlinear, and Soft Matter Physics|
|Publication status||Published - 2006 Nov 13|
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics