Topological phase locking in dissipatively-coupled noise-activated processes

We study a minimal model of two non-identical noise-activated oscillators that interact with each

other through a dissipative coupling. We find that the system exhibits a rich variety of dynamical

behaviors, including a novel phase-locking phenomenon that we term topological phase locking

(TPL). TPL is characterized by the emergence of a band of periodic orbits that form a torus knot

in phase space, along which the two oscillators advance in rational multiples of each other, which

coexists with the basin of attraction of the stable fixed point. We show that TPL arises as a

result of a complex hierarchy of global bifurcations. Even if the system remains noise-activated,

the existence of the band of periodic orbits enables effectively deterministic dynamics, resulting in

a greatly enhanced speed of the oscillators. Our results have implications for understanding the

dynamics of a wide range of systems, from biological enzymes and molecular motors to engineered

electronic, optical, or mechanical oscillators.