Effective mean field approach to kinetic Monte Carlo simulations in limit cycle dynamics with reactive and diffusive rewiring

Abstract

The dynamics of complex reactive schemes is known to deviate from the Mean Field (MF) theory when restricted on low dimensional spatial supports. This failure has been attributed to the limited number of species-neighbours which are available for interactions. In the current study, we introduce effective reactive parameters, which depend on the type of the spatial support and which allow for an effective MF description. As working example the Lattice Limit Cycle dynamics is used, restricted on a 2D square lattice with nearest neighbour interactions. We show that the MF steady state results are recovered when the kinetic rates are replaced with their effective values. The same conclusion holds when reactive stochastic rewiring is introduced in the system via long distance reactive coupling. Instead, when the stochastic coupling becomes diffusive the effective parameters no longer predict the steady state. This is attributed to the diffusion process which is an additional factor introduced into the dynamics and is not accounted for, in the kinetic MF scheme.

Chimera states in population dynamics: Networks with fragmented and hierarchical connectivities

“…The positions (lattice sites) where the particles are located may or may not be first neighbors, depending on the model (see Ref. [59]). Similarly, Eq.…”

“…Direct KMC realizations on the 2D square lattice with nearest neighbor inter-actions produced intricate fractal patterns and local oscillations of the species concentrations [48]. Later on, longdistance diffusion was introduced as a mixing mechanism allowing the species to react with all particles within a specific range, thus giving them the possibility to change their places in the lattice at finite or infinite distances [59]. The model was also studied from the viewpoint of an abstract network of phases that was shown to have features of a scale-free network through calculations of the degree distribution and clustering coefficient [60].…”