This interactive visualization illustrates the dynamics of the system \(\dot{x} = xy, \dot{y} = -y - x^2\), showing how trajectories approach the center manifold (the blue curve) and then evolve slowly along it. A click on the plot adds a new starting point, and the solution is integrated using a Runge-Kutta 4 (RK4) method, with the path drawn as a brown curve. The visualization is built with D3.js, using scaleLinear for coordinate mapping and a line generator for rendering both the manifold and the trajectory.