Analysis of the biological clock of Neurospora

A dynamical system describing the circadian fluctuation of a protein (FRQ) in Neurospora cells is investigated from the bifurcation point of view. The possible phase portraits and local bifurcations are studied. The saddle-node and Hopf-bifurcation curves are determined in the plane of two parameters using the parametric representation method. The number and the stability of the stationary points are determined. Using center manifold approximation we determine the Bautin-bifurcation point numerically.