Eur. Phys. J. B (2013) 86: 277
https://doi.org/10.1140/epjb/e2013-31112-7

Regular Article

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

¹ Department of Physical Chemistry, National Center for Scientific Research “Demokritos”, 15310 Athens, Greece
² Department of Physics, University of Athens, 15771 Athens, Greece
³ Department of Molecular Biology and Genetics, Democritus University of Thrace, 68100 Alexandroupolis, Greece

^a e-mail: aprovata@chem.demokritos.gr

Received: 11 December 2012
Received in final form: 21 March 2013
Published online: 19 June 2013

Abstract

The dynamics of stochastic nonlinear kinetic schemes is known to deviate from the mean field (MF) theory when restricted on low dimensional spatial supports. This failure has been attributed to (i) the influence of the support’s spatial extension which modifies the system’s dynamics and (ii) the influence of the noise. In the current study, we introduce effective parameters, which depend on the type of the 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 it is possible to describe the spatiotemporal average concentrations of the restricted dynamics using the MF model 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 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.