Fig. 2
From: An oscillating reaction network with an exact closed form solution in the time domain
Algorithm for finding values of parameters for the two species harmonic oscillator that achieve desired oscillation characteristics. The function parameterizeOscillator takes as inputs the desired oscillator characteristics and returns the independent parameters \({\mathcal {P}} (\theta )\) for the reaction network: \(k_2, k_4, k_6, x_1(0), x_2(0)\). In essence, parameterizeOscillator inverts \(x_n (t)\) by finding the \({\mathcal {P}}\) that minimizes the squared error difference between the desired oscillations and \(x_n (t)\) for either \(n=1\) or \(n=2\). In step 2, “relaxation” (via \(\delta (t)\)) is used to address the hard constraints that \(x_n (t) \ge 0\)