{"version":"1.0","type":"rich","title":"Dynamical systems:  center manifold","description":"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.","provider_name":"VizHub AI Studio","provider_url":"https://vizhub.com","html":"<iframe src=\"https://vizhub.com/viz/0d19e0bd895b4d298c6cd1fdaacb614f?mode=embed\" width=\"960\" height=\"500\" scrolling=\"no\" frameborder=\"0\"></iframe>","width":960,"height":500,"cache_age":3600}