Seeing physics as a mountain landscape for classification of nonlinear systems

Imagine standing on top of a mountain. From this vantage point, we can see picturesque valleys and majestic ridges below, and streams wind their way downhill. If a drop of rain falls somewhere on this terrain, gravity guides it along a path until it settles in one of the valleys. The trajectory traced by this droplet is known as a flow line, a path that indicates the direction of movement determined by the landscape's gradient.