Figure 4.

The emergence of a stable limit cycle upon further increase in the parameter $k_1$. (a,b) Solution dynamics following a small perturbation about the steady state. $M_0=54$, $P_0=19$. (a) P and M are plotted against time, t. (b) Corresponding solutions (magenta lines) are plotted in the $PM$ phase plane. P nullclines (dashed blue lines), M nullclines (solid red lines), steady states (black dots). (c,d) A larger perturbation about the steady state results in a stable limit cycle. $M_0=540$, $P_0=19$. Other details as in (a,b). Equation (2) were solved numerically. (e) Intermittent oscillations: noise allows for stochastic switching between stable limit cycle and the stable steady state. P is plotted against time, t. Equation (3) were solved numerically. $k_1=1.55$. Other parameters as in Table 1.