Mathematics – Dynamical Systems
Scientific paper
2011-01-25
Physical Review E 84(1) 016227, 2011
Mathematics
Dynamical Systems
revision in response to referee reports
Scientific paper
10.1103/PhysRevE.84.016227
We study a chain of $N+1$ phase oscillators with asymmetric but uniform coupling. This type of chain possesses $2^{N}$ ways to synchronize in so-called travelling wave states, i.e. states where the phases of the single oscillators are in relative equilibrium. We show that the number of unstable dimensions of a travelling wave equals the number of oscillators with relative phase close to $\pi$. This implies that only the relative equilibrium corresponding to approximate in-phase synchronization is locally stable. Despite the presence of a Lyapunov-type functional periodic or chaotic phase slipping occurs. For chains of length 3 and 4 we locate the region in parameter space where rotations (corresponding to phase slipping) are present.
Kalmár-Nagy Tamás
Sieber Jan
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