Scaling, cluster dynamics and complex oscillations in a multispecies Lattice Lotka–Volterra Model

The cluster formation in the cyclic (4+1)-Lattice Lotka–Volterra Model is studied by Kinetic Monte Carlo simulations on a square lattice support. At the Mean Field level this model demonstrates conservative four-dimensional oscillations which, depending on the parameters, can be chaotic or quasi-periodic. When the system is realized on a square lattice substrate the various species organize in domains (clusters) with fractal boundaries and this is consistent with dissipative dynamics. For small lattice sizes, the entire lattice oscillates in phase and the size distribution of the clusters follows a pure power law distribution. When the system size is large many independently oscillating regions are formed and as a result the cluster size distribution in addition to the power law, acquires a exponential decay dependence. This combination of power law and exponential decay of distributions and correlations is indicative, in this case, of mixing and superposition of regions oscillating asynchronously.