STATIONARY PROBABILITY-DISTRIBUTION NEAR STABLE LIMIT-CYCLES FAR FROMHOPF-BIFURCATION POINTS

We obtain analytic results for the stationary probability distribution in the vicinity of a stable limit cycle for Markov systems described by a Fokker-Planck equation or a birth-death master equation. The resu lts apply best for ranges of parameters removed from Hopf bifurcation points. As a by-product, we demonstrate that there holds a Liouville-l ike theorem for the stationary probability distribution: the product o f the velocity along the limit cycle times the area of the cross secti on of the probability distribution transverse to the cycle is a consta nt. A numerical simulation of a chemical model system with a limit cyc le shows good agreement with the analytic results.