Spatio-temporal dynamics and quantification of daisyworld in two-dimensional coupled map lattices

We spatially extend the daisyworld model on a two-dimensional toroidal coupled map lattice (CML - a generalisation of cellular automata). We investigated whether this tightly coupled system of local nonlinear dynamics with bi-directional life-environment feedback can generate a specific kind of behaviour, characterised by global stability coexisting with local instability. We introduce appropriate metrics to measure the spatio-temporal dynamics of the daisyworld system. Specifically, we evaluate spatial autocorrelation using Moran's I, and local and global temporal fluctuation through the permutation entropy and the temporal standard deviation. We categorise a range of different behaviours that can arise in such scenarios, and relate them through a parameter analysis.