Ecological Oscillators in Small-World Networks*

The synchronization of oscillations in space is a ubiquitous phenomenon in several fields, and long-range correlations can arise from short-range coupling. Previous work shows that two-cycle ecological oscillators on a regular lattice undergo a second-order phase transition that falls under the Ising universality class. However, real ecological systems are unlikely to be evenly connected, as in a square lattice. In this study, we investigate the dynamics of the oscillators on a small world network. It has been shown that, even for very small values of rewiring probability, p, Ising spins undergo a mean-field transition. We will present results for maps on small-world networks and compare their behavior to that of Ising models on similar networks.