A study on stability analysis of biochemical reaction system with negative feedback regulation

In this paper, stability of a biochemical reaction system with negative feedback regulation is considered. It is well known that such a system induces a Hopf bifurcation depending on an input level or kinetic parameters. Although the eigenvalue analysis is a powerful method for evaluating the bifurcation and the stability, applying the method to a high-dimensional system with many nonlinear rate equations would be a troublesome task in model-based analysis since many hand-calculations of partial differentiation are needed to obtain a Jacobian matrix. Then, a simple and straightforward method based on Nyquist criterion is proposed. The method is a kind of describing function method, and the vector locus for the Nyquist criterion is drawn computationally by performing frequency response test for equivalent transfer function of the open loop system.