Mathematics – Dynamical Systems
Scientific paper
2010-06-29
Mathematics
Dynamical Systems
Scientific paper
We consider the behavior of a modulated wave solution to an $\mathbb{S}^1$-equivariant autonomous system of differential equations under an external forcing of modulated wave type. The modulation frequency of the forcing is assumed to be close to the modulation frequency of the modulated wave solution, while the wave frequency of the forcing is supposed to be far from that of the modulated wave solution. We describe the domain in the three-dimensional control parameter space (of frequencies and amplitude of the forcing) where stable locking of the modulation frequencies of the forcing and the modulated wave solution occurs. Our system is a simplest case scenario for the behavior of self-pulsating lasers under the influence of external periodically modulated optical signals.
Recke Lutz
Samoilenko Anatoly
Teplinsky Alexey
Tkachenko Viktor
Yanchuk Serhiy
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