CODES Dataset: coupled_oscillators

Toy dataset for the CODES benchmark (https://github.com/robin-janssen/CODES-Benchmark).

Five harmonic oscillators, coupled with linear and non-linear springs. Each oscillator has a position x_i and a velocity v_i.

The following system of equations describes the dynamics:

Position derivatives
dx1_dt = v1
dx2_dt = v2
dx3_dt = v3
dx4_dt = v4
dx5_dt = v5 

Velocity derivatives
dv1_dt = -0.1 * v1 - 2.0 * (x1 - x2) - 0.5 * (x1 - x2)**3 + 0.05 * (x3 - x1)**2
dv2_dt = -0.1 * v2 - 2.0 * (x2 - x1) - 0.5 * (x2 - x1)**3 - 2.0 * (x2 - x3) - 0.5 * (x2 - x3)**3 + 0.05 * (x4 - x2)**2
dv3_dt = -0.1 * v3 - 2.0 * (x3 - x2) - 0.5 * (x3 - x2)**3 - 2.0 * (x3 - x4) - 0.5 * (x3 - x4)**3 + 0.05 * (x5 - x3)**2
dv4_dt = -0.1 * v4 - 2.0 * (x4 - x3) - 0.5 * (x4 - x3)**3 - 2.0 * (x4 - x5) - 0.5 * (x4 - x5)**3 + 0.05 * (x1 - x4)**2
dv5_dt = -0.1 * v5 - 2.0 * (x5 - x4) - 0.5 * (x5 - x4)**3 + 0.05 * (x2 - x5)**2