Continuing an experiment in visualizing differential equations based on the traditional phase line. (See also: Part I.)
The chart shows a set of solutions to a specific differential equation in a single variable. Initially, the equation is ẋ = 1 - x². The horizontal axis represents increasing time, and the vertical axis represents values of the variable x. Each line on the chart shows the evolution of x for a specific initial value x(0). Equilibrium points, where x(t) is constant for all time, are colored red. The controls permit adjustment of the range of initial values shown, as well as the number of lines and the time increment for the horizontal axis.
Feel free to experiment with different equations and parameters. The function for ẋ should be a valid JavaScript expression. There’s no error checking, though, so be careful.
This series of visualizations continues with part III.