one cannot conclude anything definite about the stability from the linear approximation. By examining the eigenvalues of the matrix $\mathcal{M}$ for each fixed point shown in Table **I**, we find that points $P_{1,2,4-8,10}$ are unstable and point $P_{9}$ is stable only under some conditions. We cannot determine the stability properties of $P_{3}$ from the eigenvalues, and we will give the full analysis of $P_3$ in the Appendix.

Some remarks on Tab.**I**:

1.  Apparently, points $P_2$ and $P_6$ have the same eigenvalues, and the difference between these two points is just on the value of $\lambda$. As noted in the caption of Table **I**, $\lambda_*$ means that $\lambda$ can be any value, and $\lambda_a$ is just the value that makes $f(\lambda)=0$. Obviously, $\lambda_a$ is just a special value of $\lambda_*$, and point $P_6$ is a special case of point $P_2$. $P_6$ is connected with $f(\lambda)$, but $P_2$ is not. From now on, we do not consider separately the special case of $P_6$ when we discuss the property of $P_2$. Hence the value of $\lambda_a$ is contained in our discussion of$\lambda_*$.

2.  It is straightforward to check that, if $x_c=\lambda_c=0$, $y_c$ can be any value $y_*$ when it is greater than or 