Stationary waves in two-dimensional cyclic swarms

The authors extend the problem of stationary waves in cyclic swarms to two dimensions. It is shown that for the systems of linear equations describing a difference equation with periodic boundary conditions and specific conservation conditions. One can find an algorithm to solve asynchronously the systems of linear equations. Conversely, if the authors have an algorithm to solve asynchronous systems of linear equations describing a difference equation with periodic boundary conditions, they can show that the result is the solution of the same systems of linear equations under specific conservation conditions.