A system of strings and springs in three dimensions

A three-dimensional array of classical strings and springs oscillating in three dimensions is investigated with combined analytical-numerical tools. The strings are continuous and linear. The long time behavior of the system changes dramatically when the springs are changed from linear to non-linear. The equipartition of energy, even among the particles, is badly violated. The power spectrum is consistent with chaotic motion. The maximal Lyapunov exponent is vanishing within our approximation. The most remarkable finding is a certain pairing of time averages for the particles, which occurs for many initial conditions in the non-linear case.