title: Synchronization of weakly perturbed Markov chain oscillators.
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.
authors.affiliation: Ochadai Academic Production, Ochanomizu University, Tokyo, Japan.
authors.forename: Ralf
authors.initials: R
authors.lastname: Tönjes
authors.forename: Hiroshi
authors.initials: H
authors.lastname: Kori
mesh_terms: D000465:Algorithms; D001703:Biophysics / Q000379:methods*; D008390:Markov Chains; D015233:Models, Statistical; D008962:Models, Theoretical; D017711:Nonlinear Dynamics; D009991:Oscillometry / Q000379:methods*; D010825:Physics / Q000379:methods*; D013598:Systems Theory; D013997:Time Factors