It was introduced by Marc Kac and Pierre van Moerbeke (1975) and Jürgen Moser (1975) and is named after Vito Volterra.
The Volterra lattice is a special case of the generalized Lotka–Volterra equation describing predator–prey interactions, for a sequence of species with each species preying on the next in the sequence.
The Volterra lattice also behaves like a discrete version of the KdV equation.
The Volterra lattice is the set of ordinary differential equations for functions an: where n is an integer.
Usually one adds boundary conditions: for example, the functions an could be periodic: an = an+N for some N, or could vanish for n ≤ 0 and n ≥ N. The Volterra lattice was originally stated in terms of the variables Rn = -log an in which case the equations are