I have the following delay differential equation $$ \begin{align} \frac{dx_1(t)}{dt} &= \frac{1}{1 + \left(\frac{x_2(t-\tau)}{p_0}\right)^n} - \mu_m \cdot x_1(t)\\ \frac{dx_2(t)}{dt} &= x_1(t) - \mu_p \cdot x_2(t) \end{align} $$
When I now simulate this system and plot the phase plane it looks like a converging to a limit cycle. When I, however, set the initial conditions to be within the supposed limit cycle (yellow curve below), the limit cycle is crossed.
How can this be? Is this now a stable limit cycle?
The simulation was achieved with the parameter set: $\tau=18.5$, $p_0=100$, $n=5$, $\mu_m=0.03$, and $\mu_p=0.03$.