Fig. 1

(a) Bifurcation diagram for delay model. The functions β₀(τ₁) and β₁(τ₁) are defined in “Qualitative analysis” section. In the region marked ‘stable’, the positive equilibrium Q^∗ is stable. In the region marked ‘damped oscillations’, the solutions of the delay model converge steadily to the positive equilibrium as t is large enough. At Hopf Bifurcation value, the solutions of the delay model converge consistently to limit cycle. (b) Phase diagram of delay model with parameters r=0.5062, τ₁=2.5 and τ₂=1 corresponding to ‘damped oscillations’ region. (c) Sustained oscillations of protein at Hopf Bifurcation value τ₁=3.3594. (d) Phase diagram of delay model at Hopf Bifurcation value τ₁=3.3594