Curvature Driven Dynamics in Ecological Coupled Lattice Maps*

Recent work has shown that many noisy coupled lattice maps inspired by ecological metapopulation models undergo a transition to synchrony in the Ising universality class [1]. Little emphasis, however, has been placed on a comparison of the dynamics of the zero temperature Ising model and coupled lattice maps without noise. In this talk, we will demonstrate that these two systems share two properties, both of which have been well studied in the zero temperature Ising model [2,3,4]: (1) both evolve with curvature driven dynamics and, (2) both freeze into final states with probabilities agreeing reasonably well with predictions from percolation theory. On the other hand, the coupled Ricker lattice map has stable final states, that are only metastable for the zero temperature Ising model. We will conclude with implications for synchronization in ecological metapopulations.


1. A. E. Noble, J. Machta, and A. Hastings, Nat Comm, 6:6664, (2015).
2. V. Spirin, P. Krapivsky, and S. Redner, Phys. Rev. E65, 016119 (2001).
3. J. Olejarz, P. L. Krapivsky, and S. Redner, Phys. Rev. Lett.109, 195702 (2012).
4. C. Godreche and M. Pleimling, Journal of Statistical Mechanics:Theory and Experiment, Volume 2018 (2018).