Figure 12

Mechanism of PhCompBF (the brute-force phase computation scheme) in state space for the Brusselator (changes in molecule numbers for both species are monitored). This is the state-space pictorial description of PhCompBF that corresponds to Figure 11. There are two RRE solutions in this figure. The final states of the solutions in Figure 10 are fed as initial conditions to the RRE in (11) for the Brusselator. The RRE solution, whose initial and final conditions are indicated by the circle, approaches the limit cycle and almost starts tracing it, traveling clockwise. The solution indicated by the star, which is actually leading in terms of phase that indicated by the circle, has already made the rightmost turn at the end of this simulation. The circle is way behind. The actual phase shift between the two solutions has to be computed as explained in Figure 11.