Differential equation on a doughnut

Here’s a differential equation from [1] that’s interesting to play with. Even though it’s a nonlinear system, it has a closed-form solution, namely where (a, b, c) is the solution at t = 0 and Δ = 1 + a² + b² + c². The solutions lie on the torus (doughnut). If m and n are coprime integers then the solutions […] The post Differential equation on a doughnut first appeared on John D. Cook .