Phase Portrait Generator
Phase Portrait Generator creates phase portraits for 2D dynamical systems defined by \\( \dot{x} = f(x, y) \\) and \\( \dot{y} = g(x, y) \\). Enter differential equations (e.g., “x – y”, “x + y”), axis ranges, and optional initial conditions (e.g., “0,1”). The vector field and trajectories (using Euler method) are visualized with p5.js, and computational steps are shown with MathJax.
Phase Portrait Generator
This tool generates phase portraits for 2D dynamical systems defined by \\( \dot{x} = f(x, y) \\) and \\( \dot{y} = g(x, y) \\). Input the differential equations (e.g., “x – y”, “x + y”), axis ranges (e.g., “-2,2”), and optional initial conditions for trajectories (e.g., “0,1”). The vector field and trajectories are visualized using p5.js, with computational steps shown in MathJax.
Example 1: Linear System
\\( \dot{x} = x – y \\), \\( \dot{y} = x + y \\), X Range: “-2,2”, Y Range: “-2,2”, Initial: “1,0”.
Result: Spiral or saddle point behavior.
Example 2: Pendulum
\\( \dot{x} = y \\), \\( \dot{y} = -\sin(x) \\), X Range: “-3,3”, Y Range: “-2,2”, Initial: “1,0”.
Result: Oscillatory behavior around equilibrium.