Improved parameter estimation for systems with an experimentally located Hopf bifurcation

Area of Science:

• * Systems Biology
• * Nonlinear Dynamics
• * Computational Science

Background:

• * Oscillating cell-biological systems, like yeast glycolysis and the Belousov-Zhabotinsky reaction, often exhibit Hopf bifurcations.
• * System identification relies on experimental data and prior knowledge, with quenching data being valuable.
• * Incorporating prior knowledge of Hopf bifurcation locations can enhance system identification accuracy.

Purpose of the Study:

• * To develop a novel method for system identification in oscillating systems using prior knowledge of Hopf bifurcations.
• * To reformulate this prior knowledge into a standard constrained optimization problem.
• * To demonstrate the method's effectiveness using the Brusselator model.

Main Methods:

• * Reformulation of prior knowledge about Hopf bifurcations into a constrained optimization problem.
• * Over-parametrization of the original problem to introduce extra constraints.
• * Development of a method to solve the reformulated optimization problem.

Main Results:

• * The proposed method successfully integrates prior knowledge of Hopf bifurcations into time-series estimation.
• * Over-parametrization effectively reduces the search space for system identification.
• * Demonstrated advantage of the method on the Brusselator model.

Conclusions:

• * The novel method enhances system identification by leveraging prior knowledge of Hopf bifurcations.
• * The constrained optimization formulation allows application of standard solution techniques.
• * This approach offers improved accuracy and efficiency in modeling oscillating biological systems.