Figure 8
From: Phase computations and phase models for discrete molecular oscillators
The periodic solution xs(t) for the Brusselator. The periodic solution (consisting of the changes in the molecule numbers for the species X and Y) of the RRE (the continuous deterministic model) for the Brusselator. This periodic solution vector function is called xs(t). Note that the oscillating molecular system has discrete states, i.e., it has discrete numbers for the molecule numbers for each species. However, through the continuous-state limit, we have derived the RRE and CLE, which are continuous, from the original oscillator model. Therefore, entries of the periodic solution xs(t) in this figure are continuous valued. Also, in the transformation from the discrete model to the continuous one, we have chosen to stick with molecule numbers for species rather than switching to concentrations, because we would like to plot on top of each other, compare, and use in computational analysis the SSA sample paths obtained from the discrete model and sample paths and deterministic solutions obtained from the continuous models.