Mapping nonlinear lattice equations onto cellular neural networks

The authors point out that because, under certain restrictions, cellular neural networks (CNNs) come very close to some Hamiltonian systems, they are potentially useful for simulating or realizing such systems. They show how to map two one-dimensional nonlinear lattices, the Fermi-Pasta-Ulam lattice (1965) and the Toda lattice (1975), onto a CNN. For the Toda lattice, they show what happens if the signals are driven beyond the linear region of the piecewise-linear output function. Though the system is no longer Hamiltonian, numerical experiments reveal the existence of soliton solutions for special initial conditions. This interesting phenomenon is due to a special symmetry in the CNN system of ordinary differential equations