**(2) Assumption of linearization**

According to the proposed method introduced in Section 3.2, the estimating Equation (10) is linearized near *q*<sup>∗</sup>, which means that the equation assumes a stable periodic solution. However, if the solution loses stability or the Floquet multiplier goes out of the unit circle, then the assumption is void. i.e., the (1 − *μ*) term of Equation (15) is no longer zero. Therefore, in a stable periodic region, the estimated Floquet multiplier shows the exact value of unity that we intended it to be, but there is a risk of error in the unstable periodic region. Although there are some error risks when the oscillation loses stability, we can easily recognize the unstable region where the estimated Floquet multiplier is greater than 1.
