Visualization of all bistable solutions for ODE system

General bistable solutions to the two-variable system of nonlinear ordinary differential equations:

dx1/dt = h1^n /(h1^n + x2^n) - x1
dx2/dt = h2^n /(h2^n + x1^n) - x2

In the animation, x1 is labeled "U", x2 is labeled "G".

h1 and h2 are thresholds of x1 and x2, respectively. They are labeled hU and hG in the animation. n is the Hill coefficient.

All bistable solutions are inside of the volume bounded by the cyan mesh.

Bottom plane is an orthographic projection of ODE solutions. Back plane shows values of n at which specific cross-sections were taken with n ranging from 1 to 20.