Improved parameter estimation for systems with an experimentally located Hopf bifurcation

When performing system identification, we have two sources of information: experimental data and prior knowledge. Many cell-biological systems are oscillating, and sometimes we know an input where the system reaches a Hopf bifurcation. This is the case, for example, for glycolysis in yeast cells and for the Belousov-Zhabotinsky reaction, and for both of these systems there exist significant numbers of quenching data, ideal for system identification. We present a method that includes prior knowledge of the location of a Hopf bifurcation in estimation based on time-series. The main contribution is a reformulation of the prior knowledge into the standard formulation of a constrained optimisation problem. This formulation allows for any of the standard methods to be applied, including all the theories regarding the method's properties. The reformulation is carried out through an over-parametrisation of the original problem. The over-parametrisation allows for extra constraints to be formed, and the net effect is a reduction of the search space. A method that can solve the new formulation of the problem is presented, and the advantage of adding the prior knowledge is demonstrated on the Brusselator.