Ising model with memory: results and applications to synchronization in population ecology*

Synchronized oscillations in spatially extended populations can be modeled by coupled noisy, quadratic maps in the two-cycle regime. These dynamical systems exhibit a phase transition from incoherence to synchrony that is in the equilibrium Ising universality class. However individuals in real populations have phase memory that is not contained in the standard Ising model. In this work we analyze a dynamical Ising model with an additional memory term and investigate the phase transition using analytical and numerical approaches. The effective equilibrium model of this dynamical system undergoes a phase transition in the equilibrium Ising universality class with a critical temperature that increases with the strength of the memory. We present results for this system and discuss connections to coupled map systems and also to agricultural data describing oscillations in pistachio production (masting) where tree level data from an orchard in California reveals Ising critical behavior.