Stable lamprey swimming on a skeleton of unstable periodic orbits

Chaotic systems are constructed on an underlying skeleton of unstable periodic orbits. This enables them to explore large areas of phase space. Small perturbations can be used to direct their trajectories to many different loci, unlike more stable oscillators that are stuck in one orbit unless substantial changes are made to the system. It has been hypothesized that the self-regulation of a wide variety of complex systems, including living ones, may involve using small perturbations to navigate this structure of many periodic orbits. A system using this effect would be able to select from a wide repertoire of behaviors with a small control signal.;Lamprey swimming originates in groups of neurons organized into central pattern generators (CPGs), that can be modeled as a chain of loosely coupled oscillators. In the intact animal, the rhythmic bursting of motor roots contracts muscles in a coordinated fashion generating longitudinal wave we are familiar with in swimming fish. The bursting and hence contractions are coordinated by connections between the individual oscillators of the cord, and by feedback from mechanoreceptors (displacement transducers) that respond to the cord's flexing.;I hypothesize that the oscillators of lamprey central pattern generators are chaotic in isolation and that chaos is suppressed by coupling, as has recently been shown for lobster stomatogastric ganglion(155). In this case persistant transient dynamics would be much more relevant to its observed behavior than the asymptotic stability of stable limit cycle oscillators that have historically been used in central pattern generator models. I further hypothesize that the lamprey regulates locomotion through a form of chaos control, that is, by manipulating unstable periodic orbits to emphasize certain periodic orbits and deemphasize others. From the uncountable number of chaotic orbits generated by the coupled oscillators, the system could select those appropriate for the desired swimming velocity and acceleration. Because of the sensitivity of chaotic systems, only small inputs from the brainstem and mechanoreceptors would be needed to control the loci of the CPGs in phase space.