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  • Title: Synchronization of weakly perturbed Markov chain oscillators.
    Author: Tönjes R, Kori H.
    Journal: Phys Rev E Stat Nonlin Soft Matter Phys; 2011 Nov; 84(5 Pt 2):056206. PubMed ID: 22181483.
    Abstract:
    Rate processes are simple and analytically tractable models for many dynamical systems that switch stochastically between a discrete set of quasistationary states; however, they may also approximate continuous processes by coarse-grained, symbolic dynamics. In contrast to limit-cycle oscillators that are weakly perturbed by noise, in such systems, stochasticity may be strong, and topologies more complicated than a circle can be considered. Here we apply a second-order time-dependent perturbation theory to derive expressions for the mean frequency and phase diffusion constant of discrete-state oscillators coupled or driven through weakly time-dependent transition rates. We also describe a method of global control to optimize the response of the mean frequency in complex transition networks.
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