Long and stable timescales are often observed in complex biochemical networks, such as in emergent oscillations or memory. How these robust dynamics persist remains unclear, given the many stochastic reactions and shorter time scales of the underlying components. We propose a topological model with parsimonious parameters that produces long oscillations around the network boundary, effectively reducing the system dynamics to a lower-dimensional current. I will demonstrate how this can model the circadian clock of cyanobacteria, with efficient properties such as simultaneously increased precision and decreased cost. Our work presents a new mechanism for emergent dynamics that could be useful for various cognitive and biological functions.