Representing spatially extended ecological oscillators by kinetic Ising models with memory*

Synchronous behavior in spatially-extended ecological systems can be modeled by noisy, coupled oscillators. If the individual oscillators are in a two-cycle regime, the transition to synchrony as a function of noise strength and coupling strength has been shown to be in the Ising universality class [1]. On the other hand, a nearest neighbor Ising model may not provide an accurate description of non-universal properties. In this talk we will discuss the question of accurately representing a system of coupled, noisy two-cycle oscillators by an Ising model. We show that an accurate representation requires a kinetic Ising model with a self-interaction (memory) term. Even if this kinetic Ising model with memory includes only nearest-neighbor couplings in the dynamics, its equilibrium states are described by a Hamiltonian with more distant neighbor coupling and multi-spin terms. Using maximum likelihood methods we are able to infer an accurate kinetic Ising representation of synthetic data from a noisy lattice map system. We also discuss applications to field data in ecology.

1. A. E. Noble, J. Machta, and A. Hastings, Nat Comm, 6:6664, 2015.