We examine in detail the effect of a periodic perturbation upon a system undergoing a Hopf bifurcation. Particular attention is paid to the case of resonance between the natural Hopf bifurcation frequency and the perturbation frequency. It is shown that for a certain parameter range this Hopf bifurcation is modified by the perturbation to exhibit frequency (phase) pulling and locking, and the nature of this frequency locking is described. In addition, the effect of adding diffusion to the system is discussed, and it is shown that diffusive waves are possible.
ASJC Scopus subject areas
- Applied Mathematics