A popular method to visualise solutions, to qualitatively predict their behaviour as time t increases, and to get an idea whether a stationary point is stable is the combination of direction fields with [[Phase Portrait|phase portraits]]. A direction field for a [[Autonomous 2 x 2 System of First Order Ordinary Differential Equations]] is the attachment of an arrow proportional $(f_{1}(x_{1},x_{2}),f_{2}(x_{1},x_{2}))$ to some points $(x_{1},x_{2})\in\mathbb{R}^{2}$ in order to give an impression of the direction and speed of evolution. # Applications Examples: