Spatial correlation in a Lotka–Volterra reaction diffusion mechanism.

Here we study a derivative of the Lotka-Volterra reaction diffusion mechanism using the framework of molecular dynamics. First, we perform a series of simulations in one and two dimensions and we find that there exists a critical correlation length in both cases. This means that for domain lengths below this critical correlation length the system will show spatial homogeneous oscillations, whereas for systems with domain lengths larger than the critical correlation length spatial concentration gradients will emerge and the temporal oscillations will be wiped out. We then show, as a main result, that the critical correlation length is smaller in two dimensions than in one dimension, which is in contrast to what is found in, for example, the Poincaré model. [ABSTRACT FROM AUTHOR]