The stability and inertia of sign pattern matrices with entries in $\{+,-,0\}$ associated with dynamical systems of second-order ordinary differential equations $\ddot{\mathbf{x}}=A\dot{\mathbf{x}}+B\mathbf{x}$ are studied, where A and B are real matrices of order n. An equivalent system of first-order differential equations has coefficient matrix $C=\left[\begin{array}{cc}\hfill A\hfill & \hfill B\hfill \\ \hfill I\hfill & \hfill O\hfill \end{array}\right]$ of order 2n, and eigenvalue properties are considered for sign patterns $\mathcal{C}=\left[\begin{array}{cc}\hfill \mathcal{A}\hfill & \hfill \mathcal{B}\hfill \\ \hfill \mathcal{D}\hfill & \hfill O\hfill \end{array}\right]$ of order 2n, where $\mathcal{A},\mathcal{B}$ are the sign patterns of $A,B$ respectively, and $\mathcal{D}$ is a positive diagonal sign pattern. For given sign patterns $\mathcal{A}$ and $\mathcal{B}$ where one of them is a negative diagonal sign pattern, results are determined concerning the potential stability and sign stability of $\mathcal{C}$, as well as the refined inertia of $\mathcal{C}$. Applications include the stability of such dynamical systems in which only the signs rather than the magnitudes of entries of the matrices A and B are known.

具有条目的符号模式矩阵的稳定性和惯性 $\{+,-,0\}$ 与二阶常微分方程的动力系统相关 $\ddot{\mathbf{X}}=\mathrm{一种}\dot{\mathbf{X}}+乙\mathbf{X}$进行了研究，其中A和B是n阶实矩阵。一阶微分方程的等效系统具有系数矩阵$C=\left[\begin{array}{cc}\hfill \mathrm{一种}\hfill & \hfill 乙\hfill \\ \hfill \mathrm{一世}\hfill & \hfill 哦\hfill \end{array}\right]$2 n阶，特征值属性被考虑用于符号模式$\mathcal{C}=\left[\begin{array}{cc}\hfill \mathcal{一种}\hfill & \hfill \mathcal{乙}\hfill \\ \hfill \mathcal{D}\hfill & \hfill 哦\hfill \end{array}\right]$2 n阶，其中$\mathcal{一种},\mathcal{乙}$ 是符号模式 $\mathrm{一种},乙$ 分别，和 $\mathcal{D}$是一个正对角线符号模式。对于给定的符号模式$\mathcal{一种}$ 和 $\mathcal{乙}$ 其中之一是负对角符号模式，结果取决于潜在稳定性和符号稳定性 $\mathcal{C}$，以及改进的惯性 $\mathcal{C}$. 应用包括此类动态系统的稳定性，其中只知道矩阵A和B的项的符号而不是大小。