Population model with quasi-periodic clustering

We define a population lattice model with an ad hoc (non-Hamiltonian) interaction which favors clustering. Although the transition mechanism depends only on nearest neighbor configurations, the model exhibits a long range order, as shown by computer simulations. Mathematically, the problem is formulated as a non-Markovian process whose algebraic complexity rules out an exact solution in a simple closed form. But a linearized version can be fully analyzed and yields expressions for the periods of the asymptotic clustering which are in remarkably good agreement with the experiments. Simulation results and the linear analysis are presented for one- and two-dimensional models.