  We propose a novel method for fast and scalable evaluation of periodic
solutions of systems of ordinary differential equations for a given set of
parameter values and initial conditions. The equations governing the system
dynamics are supposed to be of a special class, albeit admitting nonlinear
parametrization and state nonlinearities. The method enables to represent a
given periodic solution as sums of computable integrals and functions that are
explicitly dependent on parameters of interest and initial conditions. This
allows invoking parallel computational streams in order to increase speed of
calculations. Performance and practical implications of the method are
illustrated with examples including classical predator-prey system and models
of neuronal cells.
