> [!NOTE] Definition > Let $\underline{x}'(t)=\underline{F}(\underline{x}(t))$where $\underline{F}:\mathbb{R}^{2}\to \mathbb{R}^{2},$ be an [[Autonomous 2 x 2 System of First Order Ordinary Differential Equations|autonomous 2x2 system]]. > > A stationary point of the system is a point $\underline{x}^{*}\in \mathbb{R}^{2}$ such that $\underline{F}(x^{*})=(0,0).$ # Properties **Stability**: A stationary point is [[Stable Stationary Point of Autonomous 2 x 2 System of First Order Ordinary Differential Equations|stable]] iff ... The [[Hartman-Grobman Theorem|Hartman-Grobman theorem]] asserts that the stationary point is stable iff the [[Linearisation near Stationary Point of Autonomous 2 x 2 System of First Order Ordinary Differential Equations|linearisation of the system near the stationary point]] is stable about the origin.