Non-reciprocity permits novel dynamics in living and active topological systems

Living and active systems exhibit various emergent dynamics during system regulation, growth, and motility. However, how robust dynamics arises from stochastic components remains unclear. Towards understanding this, I develop topological theories that support robust edge currents, effectively reducing the system dynamics to a lower-dimensional subspace. I will introduce stochastic networks in molecular configuration space that model different systems from a circadian clock to ring attractors. The edge localization results in new properties, e.g., the clock demonstrates increased precision with simultaneously decreased cost. Crucially, we find that unlike in quantum systems, non-reciprocity is strictly necessary for edge states and strong localization in stochastic topological systems. Our work indicates new pathways for the design and control of active systems and their dynamics.