Guiding a self-adjusting system through chaos

We study the parametric controls of self-adjusting systems with numerical models. We investigate the situation where the target dynamics changes slowly and passes through a chaotic region. We find that feedback destabilizes controls if the target is chaotic. If the control is unstable the system migrates to the closest non-chaotic target, i.e. it adapts to the edge of chaos. For weak controls the deviation between system dynamics and target is larger, but the system dynamics is less chaotic and therefore more predictable.