Mean Field Analysis of Generalized Cyclic Competitions

The mean field analysis of stochastic dynamical system allows us to gain insight into the qualitative features of their complex behavior, as well as quantitative estimates of certain aspects of their coarse-grained properties. As such, it usually furnishes a first front in approaching new dynamical systems and informs us about their stability landscape in the absence of fluctuations among other things. A knowledge of this landscape can be a valuable tool in model building for describing real world systems and provides a guiding principle for a justifiable choice of form and model parameters.

In this work, we contribute to this analysis for two generic classes of high-dimensional models that possess a cyclic symmetry in the network that specifies their stochastic dynamics at the microscopic level. Our analysis is carried out in a manner that can be readily adapted for the mean field analysis of further generalized models that possess this symmetry. Moreover, in the second class of these models, we propose a new basic process that can change the stability landscape of an existing model and, as such, endow us with potential alternatives to model systems with robust biodiverse regimes.