Algorithm 1: An algorithm for finding unstable limit cycles.

Step 1. Determine the equilibrium points $Q_0(x_0,y_0)$ and $Q_2$ of the system. Step 2. Disturb the coordinate component $y_0$ of $Q_0$ with a smaller perturbation ${\epsilon }_0$, while $x_0$ is fixed, so that the system state originating from $A_0(x_0,a_0)$ moves towards $Q_0$, where $a_0=y_0+{\epsilon }_0$. Step 3. Trigger a larger perturbation ${\delta }_0$ to $y_0$, so that the system state starting from $B_0(x_0,b_0)$ tends to $Q_2$, where $b_0=y_0+{\delta }_0$. Step 4. Select the initial condition as the midpoint $C_0$ $(x_0,\frac{a_0+b_0}{2})$ between $A_0$ and $B_0$, if an unstable limit cycle emerges, the process terminates; if not, the system state converges to $Q_0$. Step 5. Mark $C_0$ as $A_1(x_0,a_1)$ and mark $B_0$ as $B_1$ $(x_0,b_1)$, where $a_1=\frac{a_0+b_0}{2}$ and $b_1=b_0$. Then, select the initial condition as the midpoint $C_1(x_0,\frac{a_1+b_1}{2})$ between $A_1$ And $B_1$. If an unstable limit cycle emerges, the process terminates; if not, the process continues, with $A_2$ And $B_2$, $A_3$ And $B_3$, …, until an unstable limit cycle emerges.