We study the dynamics of coupled phase oscillators on a two-dimensional Kuramoto lattice with periodic boundary conditions. For coupling strengths just below the transition to global phase-locking,… (More)

We study a stochastic model of infection spreading on a network. At each time step a node is chosen at random, along with one of its neighbors. If the node is infected and the neighbor is… (More)

We study phase locking in the Kuramoto model of coupled oscillators in the special case where the number of oscillators, N, is large but finite, and the oscillators' natural frequencies are evenly… (More)

We present a case study of how topology can affect synchronization. Specifically, we consider arrays of phase oscillators coupled in a ring or a chain topology. Each ring is perfectly matched to a… (More)

In 1992, a puzzling transition was discovered in simulations of randomly coupled limit-cycle oscillators. This so-called volcano transition has resisted analysis ever since. It was originally… (More)

In 1992 a puzzling transition was discovered in simulations of randomly coupled limit-cycle oscillators. This so-called volcano transition has resisted analysis ever since. It was originally… (More)