Stability of a chain of phase oscillators

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 traveling 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 traveling wave equals the number of oscillators with relative phase close to π . 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 lengths 3 and 4 we locate the region in parameter space where rotations (corresponding to phase slipping) are present

Robust simulation of lamprey tracking

Biologically realistic computer simulation of vertebrates is a challenging problem with exciting applications in computer graphics and robotics. Once the mechanics of locomotion are available it is interesting to mediate this locomotion with higher level behavior such as target tracking. One recent approach simulates a relatively simple vertebrate, the lamprey, using recurrent neural networks to model the central pattern generator of the spine and a physical model for the body. Target tracking behavior has also been implemented for such a model. However, previous approaches suffer from deficiencies where particular orientations of the body to the target cause the central pattern generator to shutdown. This paper describes an approach to making target tracking more robust. © Springer-Verlag Berlin Heidelberg 2006